Sarka Necasova, Antonin Novotny, Arnab Roy
We consider the motion of compressible Navier-Stokes fluids with the hard sphere pressure law around a rigid obstacle when the velocity and the density at infinity are non zero. This kind of pressure model is largely employed in various physical and industrial applications. We prove the existence of weak solution to the system in the exterior domain.
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In this paper, we rigorously derive the compressible one-fluid Navier-Stokes equation from the scaled compressible two-fluid Navier-Stokes-Maxwell equations locally in time under the assumption that the initial data are well prepared. We justify the singular limit by proving the uniform decay of the error system, which is obtained by elaborate energy estimates.
On the low Mach number limit of compressible flows in exterior moving domains
研究了有界区域外可压缩正压Navier-Stokes方程组作简单平移时解的不可压缩极限。该问题是重新制定使用的坐标变化到固定的外部域。本文利用波传播算子的谱分析，利用色散定理证明了声波的色散。不可压Navier-斯托克斯方程的解被确定为一个极限。
The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions
我们得到了半空间上具有Navier边界条件的三维可压缩等熵Navier-Stokes方程组的强解的存在性和余Sobolev正则性，当粘性参数较小时，该方程组的粘性参数在时间上是一致的.当粘性参数趋于零时，这些解在$L^2$中全局且强烈地收敛于可压缩等熵欧拉方程组的解。
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。
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 the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $Ω$. We show the convergence of the weak solution to the compressible Navier-Stokes system to the strong solution to the compressible Euler system when the viscosity and the damping coefficients tend to zero.
In this paper, we consider the initial-boundary value problem of three-dimensional isentropic compressible Navier-Stokes equations with rotating effect terms in an exterior domain with Navier-slip boundary condition and with far-field vacuum. This problem is related to the motion of the compressible viscous flow past a rotating obstacle. We establish the global existence and uniqueness of classical solutions, provided that the initial mass is small. The initial data and the angular velocity of the obstacle are allowed to have large oscillations.
We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existence of small shrinkers.
We construct forward self-similar solutions (expanders) for the compressible Navier-Stokes equations. Some of these self-similar solutions are smooth, while others exhibit a singularity do to cavitation at the origin.
An initial boundary value problem for compressible Magnetohydrodynamics (MHD) is considered on an exterior domain (with the first Betti number vanishes) in $R^3$ in this paper. The global existence of smooth solutions near a given constant state for compressible MHD with the boundary conditions of Navier-slip for the velocity filed and perfect conduction for the magnetic field is established. Moreover the explicit decay rate is given. In particular, the results obtained in this paper also imply the global existence of classical solutions for the full compressible Navier-Stokes equations with N…
The compressible Navier-Stokes equations with slip boundary conditions of friction type
本文证明了具有摩擦类型滑移边界条件的可压缩流体Navier-Stokes方程弱解的全局存在性。
Weak solutions of 3D compressible Navier-Stokes equations in critical case
该研究推导可压缩Navier-Stokes方程解的位势新估计，将其应用于临界绝热指数下的边值问题，证明了动能密度的浓度抵消，推进了临界情形下三维可压缩Navier-Stokes方程弱解的相关研究。
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。
Exterior Navier-Stokes flows for bounded data
证明了在非滑移边界条件下，在$ \mathbb{R}^{n}$中的外区域上斯托克斯方程，$n\geq 2$，在$L^{\infty}_σ$上温和解的唯一存在性.
Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system
本文对可压缩Navier-Stokes方程组的弱解引入了相对熵的概念。我们证明了对于任意一对充分光滑的检验函数，任何有限能量弱解都满足一个相对熵不等式。作为推论，我们建立了可压缩Navier-Stokes方程组的弱-强唯一性原理。
In this paper, we study the low Mach number limit of the full compressible Navier-Stokes equations with revised Maxwell law. By applying the uniform estimation of the error system, we prove that the solutions of the full compressible Navier-Stokes equations with time relaxation converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.
The full compressible Navier-Stokes system (FNS) describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid in a three-dimensional (3D) exterior domain is studied. For the initial-boundary-value problem with the slip boundary conditions on the velocity and the Neumann one on the temperature, it is shown that there exists a unique global classical solutions with the initial data which are of small energy but possibly large oscillations. In particular, both the density and temperature are allowed to vanish initially. This is the first result about classical…
We obtain the global large solutions to the compressible Navier-Stokes equations in $\mathbb{R}^2$. The solution is large in the sense that there is no smallness assumption applied to one component of the initial incompressible velocity.
Homogenization of the two-dimensional evolutionary compressible Navier-Stokes equations
研究二维穿孔区域内极小孔洞亚临界情形下演化可压缩Navier-Stokes方程的均匀化，证明密度与速度收敛至非穿孔区域的解。
We show the weak-strong uniqueness property for the compressible Navier-Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter solution exists.
Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary
研究了一维可压缩Navier-斯托克斯方程的自由边界问题。在一定的小尺度条件下，建立了粘性激波的渐近稳定性。证明是由一个基本的能量估计。
Energy conservation for the weak solutions of the compressible Navier-Stokes equations
本文在一定条件下证明了可压缩Navier-斯托克斯方程的弱解在任意时刻$t>0$的能量守恒性。所得结果对常粘性方程的重整化解和退化粘性方程的弱解都成立。我们的条件不取决于尺寸。常粘性可压缩Navier-斯托克斯方程在真空下能量守恒。我们的结果是第一个关于可压缩Navier-斯托克斯方程弱解能量守恒的结果。
On the large-distance asymptotics of steady state solutions of the Navier-Stokes equations in 3D exterior domains
我们确定的首项描述的行为在大的距离的Navier-斯托克斯方程的稳定状态的解决方案在三维外部域与消失的速度在空间无穷远。
Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain
本文建立了有界区域上完全可压缩Navier-Stokes-Maxwell方程组的强解关于马赫数和介电常数的一致估计。基于这些一致估计，我们得到了充分准备的数据的完全可压缩Navier-Stokes-Maxwell系统的不可压缩磁流体动力学方程的收敛性。
In this paper, we investigate the compressible Navier-Stokes equations with degenerate, density-dependent, viscosity coefficient driven by multiplicative stochastic noise. We consider three-dimensional periodic domain and prove that the family of weak martingale solutions is sequentially compact.
We are concerned about the barotropic compressible Navier-Stokes equations with density-dependent viscosities which may degenerate in vacuum. We show that any classical solution to barotropic compressible Navier-Stokes equations in bounded domains will blow up, when the initial density admits an isolated mass group and the viscousity coefficients satisfy some conditions. A new condition on viscosities is first put forward in this paper.
Global weak solutions to compressible quantum Navier-Stokes equations with damping
在三维空间中，利用大数据证明了带阻尼项的正压可压缩量子Navier-斯托克斯方程弱解的整体存在性。该模型由具有退化粘性的可压缩Navier-斯托克斯方程和一个非线性三阶微分算子组成，其中包含量子Bohm势和阻尼项。利用Faedo-Galerkin方法和紧性论证，证明了该方程组的整体弱解.该方程组也是可压缩Navier-斯托克斯方程的一个重要的近似方程组。这将有助于我们证明三维空间中具有退化粘性的可压缩Navier-斯托克斯方程整体弱解的存在性。
Blow-up of solutions for relaxed compressible Navier-Stokes equations
本文证明了松弛可压缩Navier-Stokes模型在大数据下的解发生爆破，避免了达到双曲性边界，改进了先前结果并通过示例对比说明了松弛效应。
On the existence of solutions to the planar exterior Navier Stokes system
本文考虑定常不可压Navier斯托克斯方程在圆盘B外的解，圆盘上的Dirichlet边界条件为非零，无穷远处的边界条件为零.证明了无对称边界条件的开集解的存在性。
On the steady Navier--Stokes equations in 2D exterior domains
研究二维外区域定常Navier-Stokes方程组的边值问题.我们证明了这个问题的任何解的有限狄利克雷积分是一致有界的。在零总通量假设下证明了解的存在性定理。
This paper presents a new approach to the local well-posedness of the $1d$ compressible Navier-Stokes systems with rough initial data. Our approach is based on establishing some smoothing and Lipschitz-type estimates for the $1d$ parabolic equation with piecewise continuous coefficients.
Global solutions and uniform convergence stability for compressible Navier-Stokes equations with oldroyd-type constitutive law
本文研究具有Oldroyd型本构律的一维等熵可压缩Navier-Stokes方程，通过建立关于松弛时间的一致先验估计，证明了小初始数据下光滑解的全局存在性，并得出系统向经典方程的全局时间收敛性。
The initial boundary value problems for compressible Navier-Stokes-Poisson is considered on a bounded domain in $\mathbb{R}^3$ in this paper. The global existence of smooth solutions near a given steady state for compressible Navier-Stokes-Poisson with physical boundary conditions is established with the exponential stability. An important feature is that the steady state (except velocity) and the background profile are allowed to be of large variation.
Weak-strong uniqueness for the isentropic compressible Navier-Stokes system
证明了环面上等熵可压缩Navier-Stokes方程组的弱-强唯一性结果。换句话说，我们给出了强解在一类弱解中唯一的条件。改进了已有的弱-强唯一性结果。这个方程的经典唯一性结果自然遵循。
In this paper, we construct a class of global large solution to the compressible Navier-Stokes equations in the whole space $\R^d$. Precisely speaking, our choice of special initial data whose $\dot{B}^{-1}_{\infty,\infty}$ norm can be arbitrarily large, namely, $||u_0||_{\dot{B}^{-1}_{\infty,\infty}}\gg 1$, allows to give rise to global-in-time solution to the compressible Navier-Stokes equations.
Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$. We prove the enhanced dissipation phenomenon for the linearized isentropic compressible Navier-Stokes equations around the Couette flow $(y, 0, 0)^\top$. Moreover, the lift-up phenomenon is also shown in this paper. Compared with the 3D incompressible Navier-Stokes equations [Ann. of Math.,185(2017), 541--608], the lift-up effect here is stronger due to the loss of the incompressible condition.
Blowup of Smooth Solutions to the Navier-Stokes Equations for Compressible Isothermal Fluids
结果表明，当初始密度为紧支集时，一维或二维径向对称等温可压缩Navier-Stokes方程组不存在非平凡整体光滑解.这一结果是Xin的工作\cite{Xin98}在等温情况下的推广。
In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many literatures concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum.
Homogenization of the compressible Navier-Stokes equations in domains with very tiny holes
本文考虑三维有界多孔区域中可压缩Navier-斯托克斯方程的均匀化问题。当孔洞数目增加到无穷大时，我们证明了，如果孔洞的尺寸足够小，则在齐次区域--无孔洞区域中，齐次化方程与可压缩Navier-斯托克斯方程相同。这与前人对斯托克斯方程和定常Navier-斯托克斯方程的研究结果一致。这是在非定常正压可压缩环境中的第一个此类结果。主要的技术新颖性是在非Lipschitz域中的Bogovskii算子的研究。
We show the uniqueness of particle paths of a velocity field, which solves the compressible isentropic Navier-Stokes equations in the half-space $\mathbb{R}_+^3$ with the Navier boundary condition. In particular, by means of energy estimates and the assumption of small energy we prove that the velocity field satisfies the necessary regularity needed to prove the uniqueness of particle paths.
Global well-posedness of the two-dimensional exterior Navier-Stokes equations for non-decaying data
证明了二维外Navier-斯托克斯方程在有限狄利克雷积分的有界初值下，在非滑移边界条件下的整体适定性.作为一个应用，我们构造全局解渐近常数的初始数据和任意大的雷诺数。
In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier-Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale geophysical motions that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations to the compressible Primitive Equations. This is the first work to use relative entropy inequality for proving hydrostatic approximation and derive the…
A fluid-particle model is investigated in the present paper, which consists of the compressible Navier-Stokes equations coupled with the Vlasov equation though a nonlinear drag force. We consider the initial value problem for the one-dimensional compressible Navier-Stokes-Vlasov system and establish the global existence and uniqueness of the weak solution for general initial data in either spatial periodic domain or spatial real line, which is shown to be a classical solution for regular initial data.
Motivated by \cite{CG10,CZ6}, we prove the global existence of solutions to the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data which are slowly varying in one direction and with initial density being away from vacuum. In particular, we present examples of initial data which generate unique global smooth solutions to 2D compressible Navier-Stokes equations with constant viscosity and with initial data which are neither small perturbation of some constant equilibrium state nor of small energy.
In this paper, we establish the existence and uniqueness of local strong solutions to the kinetic Cucker--Smale model coupled with the isentropic compressible Navier--Stokes equation in the whole space. Moreover, the blowup mechanism for strong solutions to the coupled system is also investigated.
Global well-posedness for the full compressible Navier-Stokes equations
本文主要研究索伯列夫空间中完全可压缩Navier-斯托克斯方程的Cauchy问题。利用Friedrich方法和紧性论证，我们在小初值条件下建立了方程的整体适定性。
One New Blowup Criterion for the 2D Full Compressible Navier-Stokes System
建立了二维完全可压缩Navier-Stokes方程组的爆破准则。该判据仅根据速度场的发散度给出，与温度无关。这与正压情况下的结果基本相同。
In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the domain. This is the first mathematical analysis of a compressible fluid-rigid body system where Navier-slip boundary conditions are considered. We prove existence of a weak solution of the fluid-structure system up to collision.
About the barotropic compressible quantum Navier-Stokes equations
本文研究了具有线性密度依赖粘性的正压可压缩量子Navier-斯托克斯方程及其在标度Planck常数为零时的极限。在最近关于退化可压缩Navier-斯托克斯方程的工作之后，我们利用接近真空的奇异压力证明了整体弱解的存在性。对于这种奇异压力，我们可以使用整体弱解的标准定义，当标度普朗克常数由$ε$表示趋于0时，该定义也允许证明极限。
We consider a sufficient condition for the energy conservation law of a weak solution for the full compressible Navier-Stokes equations on the torus. We prove that a weak solution constructed by Feireisl with certain integrability conditions conserve the energy. Our assumption relaxes the regularity condition for the density compared with existing results.
One-dimensional Compressible Navier-Stokes Equations with Temperature Dependent Transport Coefficients and Large Data
本文研究了一维可压缩Navier-斯托克斯方程的Cauchy问题的大数据整体光滑非真空解，该方程的迁移系数与温度有关，并满足动力学理论中的条件。得到了Nishida-Smoller型结果。
Global well-posedness of compressible Navier-Stokes equations for some classes of large initial data
证明了三维可压缩Navier-斯托克斯方程在几类大初值条件下的整体适定性，即密度具有大的振荡性，速度具有大的能量.充分利用了系统的结构（特别是有效粘性通量）。
A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations
我们提供了一个严格的推导的可压缩雷诺系统作为一个奇异的限制的可压缩（正压）Navier-Stokes系统上的薄域。特别是，非齐次边界条件的Navier-Stokes系统的解的存在性，可能是独立的利益。我们的方法是基于新的先验界限可用于硬球型的压力法。最后，在一维情形下证明了极限问题的唯一性.
The existence of dissipative solutions to the compressible isentropic Navier-Stokes equations was established in this paper. This notion was inspired by the concept of dissipative solutions to the incompressible Euler equations of Lions (\cite{Lions-1996}, Section 4.4). Our method is to recover such solutions by passing to the limits from approximated solutions, thanks to compactness argument.
In this paper we study the initial-boundary-value problem for the barotropic compressible magnetohydrodynamic system with slip boundary conditions in three-dimensional exterior domain. We establish the global existence and uniqueness of classical solutions to the exterior domain problem with the regular initial data that are of small energy but possibly large oscillations with constant state as far field which could be either vacuum or nonvacuum. In particular, the initial density of such a classical solution is allowed to have large oscillations contain vacuum states. Moreover, the large-time…
The existence theorem for the steady Navier--Stokes problem in exterior axially symmetric 3D domains
本文研究粘性不可压缩流体定常运动的Navier-斯托克斯方程在三维多连通边界外区域中的非齐次边值问题。我们证明了这个问题有一个解决方案的轴对称域和数据（没有任何小通量的限制）。
We consider a compressible Navier-Stokes system for a barotropic fluid with density dependent viscosity in a three-dimensional time-space domain $(0,T)\times Ω_\varepsilon$ where $Ω_\varepsilon = (0,\varepsilon)^2\times (0,1)$. We show that the weak solutions of the 3D system converges to the strong solution of the respective 1D system as $\varepsilon\rightarrow0.$
We identify a class of measure-valued solutions of the barotropic Euler system on a general (un-bounded) spatial domain as a vanishing viscosity limit for the compressible Navier-Stokes system. Then we establish the weak (measure-valued)-strong uniqueness principle, and, as a corollary, we obtain strong convergence to the Euler system on the lifespan of the strong solution.
Large time asymptotic behavior of the compressible Navier-Stokes Equations in partial Space-Periodic Domains
本文研究了三维等熵可压缩Navier-Stokes方程在部分空间周期域上的大时间行为，同时证明了在低维情况下，在适当的“压力”函数下，相关的剖面系统可以用类似的Navier-斯托克斯方程来描述。我们的证明是基于能量的方法加上一些微妙的分析相应的线性化问题。
The full compressible magnetohydrodynamic system in three-dimensional exterior domains is investigated. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature, and perfect one for the magnetic field, the global existence and uniqueness of classical solutions is established, under the condition that the initial data are of small energy but possibly large oscillations. In particular,the initial density and temperature are both allowed to vanish. Moreover, the large-time behavior of the classical solutions is also obt…
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