Well-posedness for the linearized motion of a compressible liquid with free surface boundary
Hans Lindblad
本文研究可压缩流体自由表面的运动问题。我们证明了线性化方程的存在性。
We study the problem of the motion of the free surface of a compressible fluid. We prove existence for the linearized equations.
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We consider the asymptotic behavior as time goes to infinity of the $L^{2}$-norm of the velocity of the linearized compressible Navier-Stokes equations in ${\bf R}^{n}$ ($n \geq 2$). As an application we shall study the optimality of the decay rate for the $L^{2}$-norm of the velocity by deriving the decay estimate from below as time goes to infinity.
This paper studies the linearized problem for the compressible Navier-Stokes equation around space-time periodic state in an infinite layer of $\mathbb{R}^n$ ($n=2,3$), and the spectral properties of the linearized evolution operator is investigated. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the asymptotic expansions of the Floquet exponents near the imaginary axis for the Bloch transformed linearized problem are obtained for small Bloch parameters, which would give the asymptotic leading part of the linearized solution operator as $t\rightarrow\infty$.
Local energy decay of solutions to the linearized compressible viscoelastic system around motionless state in an exterior domain
本文研究三维外区域中围绕静止状态的线性化可压缩黏弹性系统解的大时间行为，推导局部能量衰减估计以揭示由声波黏性扩散和弹性剪切波引起的扩散波现象。
Zero viscosity and thermal diffusivity limit of the linearized compressible Navier-Stokes-Fourier equations in the half plane
研究了半平面中可压缩粘性导热流体的线性化Navier-Stokes-Fourier方程初边值问题的零粘性和导热极限。我们考虑的情况下，粘度和热扩散率收敛到零，在相同的顺序。本文首先利用多尺度分析方法，形式化地分析了带内、边界展开项的线性化Navier-Stokes-Fourier方程的近似解。然后用能量方法得到了该方程的近似解的误差项的逐点估计，从而建立了线性化Navier-Stokes-Fourier方程在零粘性和零导热极限下的一致稳定性.本文基于\cite{xy}，将等熵情况下的结果推广到具有热扩散效应的一般可压缩流体。在\cite{xy}中，除了粘性层外，还出现了热层，热层与粘性层呈线性耦合。
In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet boundary conditions and with interior controls. We prove that the system is not null controllable at any time using localized controls in density and stress equations and even everywhere control in the velocity equation. However, we show that the system is null controllable at any time if the control acting in the density or stress equation is everywhere in the …
We consider a compressible flow structure interaction (FSI) PDE system which is linearized about some reference rest state. The deformable interface is under the effect of an ambient field generated by the underlying and unbounded material derivative term which further contributes to the non-dissipativity of the FSI system, with respect to the standard energy inner product. In this work we show that, on an appropriate subspace, only one dimension less than the entire finite energy space, the FSI system is wellposed, and is moreover associated with a continuous semigroup which is \emph{uniforml…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and its associated state equation for the associated pressure variable, each evolving within a three dimensional domain $\mathcal{O}$, are coupled to a fourth order plate equation which holds on a flat portion $% Ω$ of the boundary $\partial \mathcal{O}$. Moreover, since this coupled PDE model is the result of a linearization of the compressible Navier-Stokes equ…
Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations
针对全空间线性化可压缩 Navier-Stokes 方程，提出以 $|\mathbb{B}_0|=0$ 为阈值刻画低维最优增长与衰减，并给出加权 $L^1$ 初值解的大时间渐近轮廓。
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation which describes the time evolution of the discontinuity front of the vortex sheet. In agreement with the classical stability analysis, the problem is weakly stable if $|[v\cdotτ]|>2\sqrt{2}\,c$, and the well-posedness was obtained in standard weighted Sobolev spaces. The aim of the present paper is to improve the result of [10], by showing the existence of the s…
We consider a linearized compressible flow structure interaction (FSI) PDE model with a view of analyzing the stability properties of both the compressible flow and plate solution components. In our earlier work, we gave an answer in the affirmative to question of uniform stability for finite energy solutions of said compressible flow-structure system, by means of a ``frequency domain'' approach. However, the frequency domain method of proof in that work is not ``robust'' (insofar as we can see), when one wishes to study longtime behavior of solutions of compressible flow-structure PDE models …
We address semigroup well-posedness for a linear, compressible viscous fluid interacting at its boundary with an elastic plate. We derive the model by linearizing the compressible Navier-Stokes equations about an arbitrary flow state, so the fluid PDE includes an ambient flow profile $\mathbf{U}$. In contrast to model in [Avalos, Geredeli, Webster, 2017], we track the effect of this term at the flow-structure interface, yielding a velocity matching condition involving the material derivative of the structure; this destroys the dissipative nature of the coupling of the dynamics. We adopt here a…
Structural Stability of Supersonic Contact Discontinuities in Three-Dimensional Compressible Steady Flows
本文研究了三维可压缩等熵定常流中超音速接触间断的结构非线性稳定性。基于弱线性稳定性结果和作者在J. Diff.当量ag 255（2013），对于满足一定稳定性条件的超音速接触间断处的三维可压缩等熵定常方程的线性化问题，我们首先通过探索涡量的行为，得到了高阶范数下线性化问题解的驯服估计。由于超声速接触间断仅是弱线性稳定的，因此线性化问题解的tame估计对于背景状态和初始数据都失去了正则性，因此，为了使用Tame估计来研究非线性问题，我们采用Nash-Moser-Hörmander迭代方案来得出结论，在三个非线性系统中，三维可压缩定常流在结构上也是非线性稳定的。
Asymptotic Properties of Linearized Equations of Low Compressible Fluid Motion
考虑有界区域中粘性正压流体线性化运动方程的初边值问题。得到了该问题弱解的存在唯一性和估计。研究了当可压缩性趋于零时解向不可压缩极限的收敛性。
Incompressible limit for the compressible flow of liquid crystals
在有界区域内研究了低马赫数下液晶可压缩流动与不可压缩流动之间的联系。特别地，当马赫数趋于零时，证明了可压缩液晶流的弱解收敛于不可压缩液晶流的弱解，即证明了有界区域上的弱解的不可压缩极限.
The present paper is dedicated to the global large solutions and incompressible limit for the compressible flow of liquid crystals under the assumption on almost constant density and large volume viscosity. The result is based on Fourier analysis and involved so-called critical Besov norm.
Our objective is to study the observability and unique continuation property of the adjoint of a linearized compressible fluid structure interaction model in a 2D channel. Concerning the structure we will consider a damped Euler-Bernoulli beam located on a portion of the boundary. In the present article we establish an observability inequality for the adjoint of the linearized fluid structure interaction problem under consideration which in principle is equivalent with the null controllability of the linearized system. As a corollary of the derived observability inequality we also obtain a uni…
Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three
本文考虑了简化的可压缩液晶流动的初边值问题，在$Ω\subset\mathbb R^3$中进行了数值模拟。我们建立了整体弱解的存在性，提供的初始取向指向矢场$d_0$位于半球$\mathbb S^2_+$。
Incompressible Limit of the Compressible Nematic Liquid Crystal Flow
本文研究了R^N（N = 2，3）中具有周期边界条件的液晶可压缩流体力学流动的不可压缩极限。严格证明了可压缩方程组的局部（和整体）强解收敛于不可压缩方程组的局部（和整体）强解。此外，还得到了一定意义下的收敛速度。
Long-time Behavior of Solution for the Compressible Nematic Liquid Crystal Flows in $\mathbb{R}^3$
本文研究三维全空间中可压缩液晶流动的柯西问题。首先，我们用谱分析和能量估计的方法建立了可压缩液晶流的时间衰减率。此外，我们还提高了密度、速度和指向矢的高阶空间导数的收敛速度。最后，还建立了解的混合时空导数的时间衰减率。
Global weak solution and large-time behavior for the compressible flow of liquid crystals
本文考虑了液晶可压缩流动的三维方程组。研究了有界区域上一类具有大数据量的初边值问题。通过对绝热指数$γ>\frac32$的三层近似、能量估计和弱收敛性，证明了整体弱解的存在性和大时间行为.
Blow up criterion for compressible nematic liquid crystal flows in dimension three
本文考虑三维可压缩液晶材料简化流体力学流动模型的短时强解。我们建立了一个判据，在有限时间的速度梯度的变形张量的最大范数和液晶指向矢场的梯度的最大范数的平方的时间积分方面的可能崩溃的解决方案。
Incompressible Limit of a Compressible Liquid Crystals System
本文研究了可压缩液晶系统解的不可压缩极限。我们在整个空间$\mathbb{R}^{\mathbb{N}}$和$\mathbb{R}^{\mathbb{N}}$的一个有界区域上考虑问题的Dirichlet边界条件。这里的维数为$\mathbb{N}=2$或3。
We study the hydrodynamics of compressible flows of active liquid crystals in the Beris-Edwards hydrodynamics framework, using the Landau-de Gennes $Q$-tensor order parameter to describe liquid crystalline ordering. We prove the existence of global weak solutions for this active system in three space dimensions by the three-level approximations and weak convergence argument. New techniques and estimates are developed to overcome the difficulties caused by the active terms.
The present paper considers a homogeneous bubble inside an unbounded polytropic compressible liquid with viscosity. The system is governed by the Navier-Stokes equation with free boundary which is determined by the kinematic and dynamic boundary conditions on the bubble-liquid interface. The global existence of solution is proved, and the $\dot{H}^1$ asymptotic stability of the spherical equilibrium in terms of viscous damping together with a explicit decay rate is given in bare energy methods.
A Beale--Kato--Majda criterion for the 3-D Compressible Nematic Liquid Crystal Flows with Vacuum
本文证明了具有非负初始密度的三维可压缩液晶流的强解的Beale-Kato-Majda爆破准则。更精确地说，强解存在的整体，如果$L^{1}(0,T;L^{\infty})$ -范数的梯度的速度$u$是有界的。我们的判据改进了X. Liu和L. Liu（\cite{LL}，A blow-up criterion for the compressable liquid crystals system，arXiv：1011.4399v2 [math-ph] 23 Nov. 2010）.
Maximal $L_1$-regularity for the linearized compressible Navier-Stokes equations
本文研究了半空间中线性化可压缩纳维-斯托克斯方程在非滑边界条件下的$ L_1 $最大正则性，通过构造连续解析半群并证明其生成元的正则性，利用Besov空间进行分析。
Well-posedness for the Linearized Motion of an Incompressible Liquid with Free Surface Boundary
我们研究液体自由表面的运动问题。我们证明了线性化方程的存在性和稳定性。
We establish the local existence and uniqueness of solutions to the free-boundary ideal compressible magnetohydrodynamic equations with surface tension in three spatial dimensions by a suitable modification of the Nash--Moser iteration scheme. The main ingredients in proving the convergence of the scheme are the tame estimates and unique solvability of the linearized problem in the anisotropic Sobolev spaces $H_*^m$ for $m$ large enough. In order to derive the tame estimates, we make full use of the boundary regularity enhanced from the surface tension. The unique solution of the linearized pr…
Controllability and Stabilizability of the Linearized Compressible Navier-Stokes System with Maxwell's Law
本文研究了带 Maxwell 定律的线性化可压缩 Navier-Stokes 系统在周期边界下的控制性质，通过局部内部控制和单一边界控制证明了时间足够大时的精确可控性，并利用 Gramian 方法实现了任意衰减速率的指数可镇定性。
On the motion of viscous, compressible and heat-conducting liquids
本文考虑一类粘性、可压缩、导热的类液体运动的方程组，方程组的一般状态方程为Mie-Grueneisen型。此外，我们还假设，对于较大的温度值，粘滞系数可能衰减到零。证明了该方程的整体时间弱解的存在性，得到了一个相对的能量不等式，并比较了相同初值下的弱解与强解的弱强唯一性.
We prove the existence of a weak solution to a non-isothermal compressible model for nematic liquid crystals. An initial-boundary value problem is studied in a bounded domain with large data. The existence of a global weak solution is established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent γ>3/2.
We address semigroup well-posedness of the fluid-structure interaction of a linearized compressible, viscous fluid and an elastic plate (in the absence of rotational inertia). Unlike existing work in the literature, we linearize the compressible Navier-Stokes equations about an arbitrary state (assuming the fluid is barotropic), and so the fluid PDE component of the interaction will generally include a nontrivial ambient flow profile $ \mathbf{U}$. The appearance of this term introduces new challenges at the level of the stationary problem. In addition, the boundary of the fluid domain is unav…
Global Low-Energy Weak Solution and Large-Time Behavior for the Compressible Flow of Liquid Crystals
本文考虑简化Ericksen-Leslie方程组在$\mathbb R^3$中的弱解。当$L^2$中的初始数据较小且初始密度为正且本质有界时，我们首先证明了$\mathbb R^3$中整体弱解的存在性.建立了整体弱解的大时间性态。
A regularity result for the free boundary compressible Euler equations of a liquid
针对无表面张力的液体自由边界可压缩欧拉方程，提出新加权函数框架并利用Hardy不等式改善流映射正则性，通过分解初始密度函数实现，无需高阶波动方程。
We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of Euler's equations in Lagrangian coordinates which satisfies uniform energy estimates as the smoothing parameter goes to zero. The main technical tools are delicate energy estimates and optimal elliptic estimates in terms of boundary regularity, for the Dirichlet problem and Green's function.
We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case \cite{Jiang-Luo-arXiv-2017} and some techniques from compressible Navier-Stokes equations, we prove the local-in-time existence of the classical solution to the system with finite initial energy, under some constraints on the Leslie coefficients which ensure the basic energy law is dissipative. Furthermore, with an additional assumption on the coefficients which provides a damping effect, and the smallness of the initial energy, the global classical solut…
Time periodic solutions of compressible fluid models of Korteweg type
研究了$\mathbb{R}^n$中受时间周期外力作用的可压缩Navier-Stokes-Korteweg方程组时间周期解的存在性、唯一性和时间渐近稳定性.我们的分析是基于能量方法和线性化系统的解决方案的时间衰减估计的组合。
Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity
针对三维可压缩液晶流具有密度依赖粘性的柯西问题，证明当粘性系数为密度幂函数（幂次>1）、初始密度足够大且初始指向矢导数$L^3$范数足够小时，系统存在唯一整体强解，首次实现无速度小性假设的三维结果。
We derive a priori estimates for the compressible free-boundary Euler equations with surface tension in three spatial dimensions in the case of a liquid. These are estimates for local existence in Lagrangian coordinates when the initial velocity and initial density belong to $H^3$, with an extra regularity condition on the moving boundary, thus lowering the regularity of the initial data. Our methods are direct and involve two key elements: the boundary regularity provided by the mean curvature, and a new compressible Cauchy invariance.
Global existence and incompressible limit in critical spaces for compressible flow of liquid crystals
在临界空间框架下，研究了双折射液晶可压缩流动的柯西问题。我们首先建立了整体解的存在性和唯一性，只要初始数据接近某些平衡态。这一结果改进了Hu和Wu的工作[SIAM J. Math. Anal.，45（2013），pp. 2678-2699]通过放松初始数据在指向矢场方面的规则性要求。然后，我们考虑的不可压缩极限问题，准备不良的初始数据。我们证明了当马赫数趋于零时，液晶可压缩流动的整体解在某些函数空间收敛于相应的不可压缩模型的解。此外，还得到了精确的收敛速度。
In this paper, we prove a new type of energy estimates for the compressible Euler's equation with free boundary, with a boundary part and an interior part. These can be thought of as a generalization of the energies in Christodoulou and Lindblad [CL] to the compressible case and do not require the fluid to be irrotational. In addition, we show that our estimates are in fact uniform in the sound speed. As a consequence, we obtain convergence of solutions of compressible Euler equations with a free boundary to solutions of the incompressible equations, generalizing the result of Ebin [Eb] to whe…
Global solution to the three-dimensional compressible flow of liquid crystals
研究三维向列型液晶可压缩流的柯西问题，在临界Besov空间中证明了当初始数据接近平衡态时全局强解的存在唯一性，通过局部适定性和一致估计获得结果。
Strong solutions of the compressible nematic liquid crystal flow
研究了简化Ericksen-Leslie方程组在区域$Ω\subset\mathbb R^3$中的可压缩双折射液晶流动的强解.我们首先证明了局部存在唯一的强解，只要初始数据$ρ_0, u_0, d_0$是充分正则的，并满足自然相容条件。初始密度函数$ρ_0$可以在开子集上消失（即，可能存在初始真空）。然后，我们证明了这样的局部强解在有限时间爆破的数量$\|ρ\|_{L^\infty_tL^\infty_x}$和$\|\nabla d\|_{L^3_tL^\infty_x}$方面的可能崩溃的一个标准。
In this paper, we study the uniform regularity and vanishing viscosity limit for the compressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the compressible nematic liquid crystal flows with boundary condition in a finite time interval which is independent of the viscosity coefficient. The solutions are uniform bounded in a conormal Sobolev space. Furthermore, we prove that the density and velocity are uniform bounded in $W^{1, \infty}$, and the director field is uniform bounded in $W^{3,\infty}$ respectively. B…
In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established under the condition that the scaling invariant quantity $ (\|ρ_0\|_\infty+1)\big[\|ρ_0\|_3+(\|ρ_0\|_\infty+1)^2(\|\sqrt{ρ_0}u_0\|_2^2+ \|\nabla d_0\|_2^2)\big] \big[\|\nabla u_0\|_2^2+(\|ρ_0\|_\infty+1)(\|\sqrt{ρ_0}E_0\|_2^2 + \|\nabla^2 d_0\|_2^2)\big]$ is sufficiently small with the smallness depending only on the parameters appeared in the system.
In this paper, we consider the compressible fluid model of Korteweg type which can be used as a phase transition model. It is shown that the system admits a unique, global strong solution for small initial data in $\mathbb R^N$, $N \geq 3$. In this study, the main tools are the maximal $L_p$-$L_q$ regularity and $L_p$-$L_q$ decay properties of solutions to the linearized equations.
Incompressible limit of the Ericksen-Leslie hyperbolic liquid crystal model in compressible flow
本文在经典解框架下研究可压缩Ericksen-Leslie抛物-双曲液晶模型的不可压缩极限，通过引入惯性常数并建立关于Mach数一致的能量估计，证明了不可压缩系统全局经典解的存在性并给出收敛速率。
We study the three-dimensional compressible Navier-Stokes equations coupled with the $Q$-tensor equation perturbed by a multiplicative stochastic force, which describes the motion of nematic liquid crystal flows. The local existence and uniqueness of strong pathwise solution up to a positive stopping time is established where ``strong" is in both PDE and probability sense. The proof relies on the Galerkin approximation scheme, stochastic compactness, identification of the limit, uniqueness and a cutting-off argument. In the stochastic setting, we develop an extra layer approximation to overcom…
The aim of this paper is to develop the general $L_p$ theory for the barotropic compressible Navier-Stokes equations with the free boundary condition in the exterior domain in $\mathbb{R}^N$ ($N\geq 3$). By the spectral analysis, we obtain the classical $L_p$-$L_q$ decay estimate for the linearized model problem (with variable coefficients) in view of the partial Lagrangian transformation.
We consider a nonlocal version of the quasi-static Navier-Stokes-Korteweg equations with a non-monotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapour state. For a porous domain that is perforated by cavities with diameter proportional to their mutual distance the homogenization limit is analyzed. We extend the results for compressible one-phase flow with polytropic pressure laws and prove that the effective motion is governed by a nonlocal version of the Cahn-Hilliard equation. Crucial for the analys…
Small data global regularity for simplified 3-D Ericksen-Leslie's compressible hyperbolic liquid crystal model
本文针对三维可压缩Ericksen-Leslie双曲液晶模型，结合向量场方法与傅里叶分析，利用不同频率下密度与速度场衰减特性的差异，证明了平衡态附近小光滑初值的全局正则性。
The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the equation of the active particles. The existence of weak solutions to the stationary problem is established through a two-level approximation scheme, compactness estimates and weak convergence arguments. Novel techniques are developed to overcome the difficulties due to the lower regularity of stationary solutions, a Moser-type iteration is used to deal with the …
Global Weak Solutions to the Equations of Compressible Flow of Nematic Liquid Crystals in Two Dimensions
本文考虑二维简化Ericksen-Leslie可压缩液晶流动方程组的弱解。首先研究有界区域上的初边值问题。通过发展新的技巧和估计来克服方向场上角动量方程的超临界非线性所带来的困难，并采用标准的三层近似格式和可压缩斯托克斯方程的弱收敛性论证，我们在对初始能量施加限制的情况下建立了整体弱解的存在性，包括小初始能量的情况.然后研究了具有大初值的Cauchy问题，利用区域扩张技巧和刚性定理证明了当方向场的初值的第二分量满足一定的几何角条件时，大弱解的整体存在性.
On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain
本文研究了一类具有大初始能量的可压缩Ericksen-Leslie方程组在有界区域$Ω\subset \mathbb{R}^N$中弱解的整体存在性，其中N=2或3.利用最大值原理、Nirenberg插值不等式和对初始方向场$\mf{d}_0$的第三分量$N$施加的小条件，克服了角动量方程中超临界非线性$|\nabla{\mathbf d}|^2{\mathbf d}$引起的困难，然后采用修正的三维近似格式和可压缩Navier-斯托克斯方程的弱收敛论证，在初始密度和初始速度不满足任何小性条件的情况下，我们证明了具有大初始能量的初边值问题的整体弱解的存在性。
Global Well-Posedness with Large Oscillations and Vacuum to the Three-Dimensional Equations of Compressible Nematic Liquid Crystal Flows
本文讨论了可压缩液晶材料运动的简化流体力学三维方程。在真空或非真空的远场条件下，证明了具有小能量但可能有大振荡的光滑初值的Cauchy问题的整体经典解的存在性.初始密度可以为零，真空集的空间测度可以任意大，特别是初始密度甚至可以有紧支集。作为一个副产品，大时间行为的解决方案也进行了研究。
Linear Rayleigh-Taylor instability for viscous, compressible fluids
本文研究了可压缩Navier-斯托克斯方程线性化后的方程组，即沿平面界面上较重流体位于较轻流体上方的稳态剖面，即Rayleigh-Taylor不稳定性。我们考虑的方程有或没有表面张力，与粘度允许依赖于密度，并在周期性和非周期性的设置。在粘性的存在下，没有自然的变分框架来构造线性化问题的增长模式解。我们发展了一种研究一族修正的变分问题以产生最大增长模式的一般方法。使用这些增长模式，我们构造光滑（当限制到每个流体域）的线性方程的解决方案，在时间上呈指数增长的索伯列夫空间。然后，我们证明了任意解的线性化方程的最快可能的增长率的增长模式的估计。在周期性的设置，我们表明，足够小的周期性避免了不稳定的表面张力的存在。
Dissipative solutions to a Beris-Edwards type model for compressible active nematic liquid crystals
本文在Beris-Edwards模型框架下，证明了压缩性活性向列液晶的耗散解存在性，采用三级近似方案处理非线性粘度张量和非均匀边界条件。
Local-in-time existence of strong solutions to a class of compressible non-Newtonian Navier-Stokes equations
本文利用Weis乘子定理建立线性化方程的$L^p$理论，证明广义可压缩非牛顿Navier-Stokes方程对任意大初值数据强解的局部时间存在性，推广了Shibata和Enomoto的可压缩流体结果。
Decay estimates for the compressible viscoelastic equations in an exterior domain
针对外区域中的可压缩粘弹性方程，该研究建立线性化问题解的 $L_2$ 估计，并证明非线性问题解及其时空导数的最优 $L_2$ 衰减率。
Global Well-Posedness of Strong Solutions to the Two-Dimensional Compressible Nematic Liquid Crystal Flows with Large Initial Data and Vacuum
本文证明了二维可压缩向列型液晶流在剪切粘度为常数、体粘度满足特定幂律且$\beta>4/3$时，无需限制初值大小且允许真空，强解全局存在且唯一，且初始取向场无需几何角度条件。
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