On the steady Navier--Stokes equations in 2D exterior domains
Mikhail V. Korobkov, Konstantinas Pileckas, Remigio Russo
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。
We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence theorem under zero total flux assumption.
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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.
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。
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。
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。
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 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.
This paper treats the stationary Stokes problem in exterior domain of $\mathbb{R}^3$ with Navier slip boundary condition. The behavior at infinity of the data and the solution are determined by setting the problem in $L^p$-spaces, for $p> 2$, with weights. The main results are the existence and uniqueness of strong solutions of the corresponding system.
In this paper we investigate the uniqueness of solutions of the steady planar Navier-Stokes equations with different boundary conditions in the exterior domain. For a class of incompressible flow with constant vorticity, we prove the uniqueness of the solution under the enhanced Navier boundary conditions. At the same time, some counterexamples are given to show that the uniqueness of the solution fails under the Navier boundary conditions. For the general incompressible flow with Dirichlet boundary condition, we prove various sufficient conditions for the uniqueness of the solution.
Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain
本文研究了二维不可压Navier-斯托克斯方程在一个障碍物外的Dirichlet边界条件。假设速度在无穷远处的环量足够小，我们证明了相应的初边值问题解的大时间行为是由Lamb-Oseen涡描述的.后者是著名的Navier-Stokes方程组在全空间的显式自相似解$\R^2$。
Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain
研究了不可压缩流体在有界障碍物周围的渐近行为。在$\R^n$的外部区域中用定常Navier-斯托克斯方程和$n\ge 2$来模拟该问题。我们将证明，在某些假设下，任何非平凡的速度场服从一个最小衰减率在无穷远$\exp(-Ct^2\log t)$。我们的证明是基于适当的Carleman估计。
Global strong solutions to the inhomogeneous incompressible Navier-Stokes system in the exterior of a cylinder
本文在Dirichlet边界条件下，建立了圆柱外非齐次不可压Navier-Stokes方程组的整体强轴对称解。此外，在这些溶液中允许真空。分析的关键要素之一是获得速度场的${L^{2}(s,T;L^{\infty}(Ω))}$界，其中解的轴对称性起着重要作用。
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.
Stability of steady states of the 3-D Navier-Stokes-Poisson equations with non-flat doping profile in exterior domains
本文研究三维外部区域中带非平坦掺杂分布的可压缩Navier-Stokes-Poisson方程，通过上下解方法构造稳态并采用精细椭圆估计等新技术，建立了Navier-slip边界条件下稳态附近强解的全局存在性。
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…
Asymptotics of solutions to the Navier-Stokes system in exterior domains
本文研究了在具有$n\geq2$的$\mathbb{R}^n$的外部区域上具有Dirichlet边界条件的不可压Navier-Stokes方程.我们比较长时间的行为的解决方案，这个初边值问题的长期行为的解决方案的类似柯西问题在整个空间$\mathbb{R}^n$。我们发现，无论是在弱$L^{n}$-空间中的小初始数据的情况下，还是对于某一类大初始数据，这两个问题的解的长时间渐近性都是一致的。
Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers
我们表明，该方程的Navier-Stokes方程以及随机扰动可以从一个随机变分原理，其中的压力作为拉格朗日乘子引入。此外，我们描述了如何获得相应的运动常数。
Motivated by Gilbarg-Weinberger's early work on asymptotic properties of steady plane solutions of the Navier-Stokes equations on a neighborhood of infinity \cite{GW1978} , we investigate asymptotic properties of steady plane solutions of this system on a half-neighborhood of infinity with finite Dirichlet integral and Navier-slip boundary condition, and obtain that the velocity of the solution grows more slowly than $\sqrt{\log r}$, while the pressure converges to $0$ along each ray passing through the origin.
The nonhomogeneous Navier-Stokes equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with nonslip or slip boundary conditions. We prove that the strong solutions exists globally in time provided that the gradient of the initial velocity is suitably small. Here the initial density is allowed to contain vacuum states. Moreover, after developing some new techniques and methods, the large-time behavior of the strong solutions with exponential decay-in-time rates is also obtained.
New results for the Oseen problem with applications to the Navier-Stokes equations in exterior domains
在满索伯列夫空间中证明了$\mathbb{R}^n$，$n\ge 2$的光滑外区域中稳态Oseen问题的存在唯一性.然后，这些结果，一方面，在相应的（线性）时间周期的情况下，在研究类似的性质，另一方面，更重要的是，证明类似的性质，其非线性对应，至少对于小数据。
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.
We consider the spatial-temporal behavior of the Navier-Stokes flow past a rigid body in $\mathbb{R}^3$. The present paper develops analysis in Lebesgue spaces with anisotropic weights $(1+|x|)^α(1+|x|-x_1)^β$, which naturally arise in the asymptotic structure of fluid when the translational velocity of the body is parallel to the $x_1$-direction. We derive anisotropically weighted $L^q$-$L^r$ estimates for the Oseen semigroup in exterior domains. As applications of those estimates, we study the stability/attainability of the Navier-Stokes flow in anisotropically weighted $L^q$ spaces to get t…
$L^p$-theory for the exterior Stokes problem with Navier's type slip-without-friction boundary conditions
本文在$p>3$的$L^p$理论框架下，于加权索伯列夫空间中研究三维外域带无摩擦滑移边界条件的定常斯托克斯方程，通过获取inf-sup条件证明弱解在非平凡核内的存在唯一性。
Attractor Dimensions of Three-Dimensional Navier-Stokes-$α$ Model for Fast Rotating Fluids on Generic-Period Domains: Comparison with Navier-Stokes Equations
考虑了三维快速旋转地球物理流体的Navier-Stokes- $α$模型。Navier-Stokes- $α$模型是通过拉格朗日平均得到的精确Navier-Stokes方程斯托克斯方程的非线性色散正则化，并趋向于Navier-斯托克斯方程为$α\rightarrow 0^+$。我们估计了全局吸引子维数的上界，并研究了维数对参数$α$的依赖性。在$α$中所有的估计都是一致的，并且当$α\rightarrow 0^+$ .
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…
Global well-posedness and time-decay estimates of the Navier-Stokes equations in exterior domains for critical data
本文针对外域中Navier-Stokes方程，研究比$L^n_\sigma$更大的临界空间中小初始数据下的整体强可解性，扩展了该方程整体适定性的适用范围。
Extension of Hamel paradox for the 2D exterior Navier-Stokes problem
本文研究了二维外Navier-Stokes问题，通过在内部边界引入非零通量推广了Hamel非唯一性结果，并提出通过附加无穷远衰减条件恢复解的唯一性。
Local well-posedness of strong solutions to the compressible Navier-Stokes equations with degenerate viscosities and far field vacuum in 3D exterior domains
本文研究了三维外部领域中压缩性纳维-斯托克斯方程在粘度为密度幂函数且初始密度趋于远场真空时强解的局部适定性，方法克服了边界项和远场真空的困难，并使δ的选择与气体系数无关。
Asymptotic properties of the Stokes flow in an exterior domain with slowly decaying initial data and its application to the Navier-Stokes equations
本文研究外部区域中慢衰减初始数据下Stokes流的衰减率，并应用于Navier-Stokes方程，得到唯一强解和最优的逐点衰减估计。
Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain
研究了二维外区域中不可压Navier-斯托克斯方程在无滑移边界条件下的无限能量解的长时间行为。初始数据，我们认为是有限能量扰动的光滑涡与小循环在无穷远，但在其他任意大。使用对数能量估计和一些插值参数，我们证明了该解逼近自相似的Oseen涡旋，如$t \to \infty$。这一结果是与Yasunori Maekawa（神户大学）合作获得的。
On Caccioppoli's inequalities of Stokes equations and Navier-Stokes equations near boundary
研究了非定常斯托克斯方程和Navier-斯托克斯方程的Caccioppoli不等式.我们的分析是局部的边界附近，我们证明，与内部情况相比，Caccioppoli的斯托克斯方程和Navier-斯托克斯方程的不等式，在一般情况下，失败的边界附近。
Reductions of the Navier-Stokes-Allen-Cahn and the Navier-Stokes-Cahn-Hilliard equations
本文研究了两个著名的恒温两相流体流动模型，等温Navier-Stokes-Allen-Cahn方程和等温Navier-Stokes-Cahn-Hilliard方程，这两个方程都由流体（总）密度ρ、（质量平均）速度u和（其中一相）浓度c的方程组成。假设在任何一种情况下，这两个阶段是不可压缩的不同的密度，每个模型被证明是减少到一个系统的发展方程在ρ和u单独。在Navier-Stokes-Allen-Cahn模型的情况下，该简化系统是经典的Navier-Stokes-Korteweg模型。从Navier-Stokes-Cahn-Hilliard方程得到的约化系统是一个新的“积分”-微分系统，其中一个非局部算子作用于速度的发散。
An algebraic upper bound for the decay rate of solutions to the Navier-Stokes and Navier-Stokes-Coriolis equations in the critical space $\dot{H} ^{\frac{1}{2}} (\mathbb{R} ^3)$ is derived using the Fourier Splitting Method. Estimates are framed in terms of the decay character of initial data, leading to solutions with algebraic decay and showing in detail the roles played by the linear and nonlinear parts.
On the hydrostatic approximation of the Navier-Stokes equations in a thin strip
本文首先证明了在切向变量为小解析数据的情况下，二维条纹区域中尺度各向异性Navier-Stokes方程组和流体静力Navier-Stokes方程组的整体适定性.然后，我们证明了从各向异性的Navier-Stokes系统的静力Navier-Stokes系统的分析数据的限制。
Global Solution for the incompressible Navier-Stokes equations] { Global Solution for the incompressible Navier-Stokes equations with a class of large data in $BMO^{-1}(\mathbb{R}^3)$
本文建立了一类大周期数据$u_0 \in BMO^{-1}(\mathbb{R}^3)$的Navier-斯托克斯方程的整体适定性和时空解析性。这改进了Koch \& Tataru \cite{koch-tataru}的经典结果，即在小初始数据$u_0 \in BMO^{-1}(\mathbb{R}^n)$下的整体适定性.
Stokes and Navier-Stokes equations with Navier boundary condition
本文研究了一类有界区域$Ω\subset\mathbb{R}^{3}$中具有非齐次Navier边界条件的定常Stokes方程和斯托克斯方程。在考虑摩擦系数$α$的最小正则性的情况下，证明了所有$1<p<\infty$的弱解和强解在$\mathbf{W}^{1,p}(Ω)$和$\mathbf{W}^{2,p}(Ω)$中的存在唯一性.此外，我们推导出关于$α$的解的一致估计，这使我们能够分析解的行为时，$α\rightarrow \infty$。
In some problems of fluid mechanics, it is possible to be confronted with data that are not regular, that is why we are interested here in the search for the so-called very weak solutions for the stationary Stokes problem with Navier-type boundary conditions in a three-dimensional exterior domain. The problem describes the flow of a viscous and incompressible fluid past an obstacle where we assume that the fluid may slip on the boundary of the obstacle. Because the flow domain is unbounded, we set the problem in weighted Sobolev spaces in order to control the behavior at infinity of the soluti…
On the global regularity of axisymmetric Navier-Stokes-Boussinesq system
本文证明了具有轴对称初值的三维Navier-Stokes-Boussinesq方程组的一个整体适定性。该系统耦合了Navier-斯托克斯方程和控制密度的输运方程。
We introduce a framework to justify hydrodynamic limits of the Vlasov-Navier-Stokes system. We specifically study high friction regimes, which take into account the fact that particles of the dispersed phase are light (resp. small) compared to the fluid part, and lead to the derivation of Transport-Navier-Stokes (resp. Inhomogeneous Navier-Stokes) systems.
Stabilization of Navier - Stokes equations by oblique boundary feedback controllers
针对Navier-斯托克斯方程，设计了一种线性边界反馈控制器.
Newtonian and single layer potentials for the Stokes system with $L^{\infty}$ coefficients and the exterior Dirichlet problem
利用基于$L^2$的索伯列夫空间中某些问题的混合变分形式，定义了${\mathbb R}^3$中Lipschitz域上具有$L^{\infty}$系数的Stokes系统的牛顿势和层势.然后利用这些势和相应的单层算子的逆，给出了具有$L^{\infty}$系数的Stokes系统的外狄利克雷问题的解.
Local Regularity of Axisymmetric Solutions to the Navier-Stokes Equations}
本文证明了三维非定常Navier-斯托克斯方程轴对称解的局部正则性条件。它表明，Navier-斯托克斯方程的轴对称能量解没有I型爆破。
Space-time holomorphic solutions of Navier-Stokes equations
引入了偏微分方程时空全纯解的概念，构造了Navier-斯托克斯方程的亚纯解.
The energy equality for the Navier-Stokes equations in bounded domains
本文给出了有界区域上不可压Navier-斯托克斯方程能量相等的一个充分条件。
On the large time $L^{\infty}$-estimates of the Stokes semigroup in two-dimensional exterior domains
证明了Stokes半群是二维外部区域上具有角$π/2$的$L^{\infty}_σ$上的有界解析半群.这个结果是由Borchers和Varnhorn（1993）建立的$p\in (1,\infty)$半群的$L^{p}$ -有界性的端点情况，也是作者和Giga（2014）研究的有限时间$L^{\infty}$ -估计的扩展。证明是基于有界稳定流的不存在性结果（斯托克斯悖论）和斯托克斯预解式的净力的一些渐近公式。
Estimates of time-periodic fundamental solutions to the linearized Navier-Stokes equations
研究了$n\geq 2$中Navier-斯托克斯方程的时间周期Stokes和Osen线性化的基本解.可积性和逐点估计的建立。
Sturmian Multiple Zeros for Stokes and Navier--Stokes Equations in $\re^3$ via Solenoidal Hermite Polynomials
三维Stokes和Navier-斯托克斯方程的多重空间零点形成是根据螺线管Hermite多项式的节点集而发生的。讨论了带双调和粘性算子的适定Burnett方程的推广。
Gevrey stability of hydrostatic approximate for the Navier-Stokes equations in a thin domain
本文证明了在$x$中，对于Gevrey 9/8正则的凸初值，从薄区域的Navier-Stokes方程组到流体静力Navier-Stokes/Prandtl方程组的极限。
These notes are dedicated to the analysis of the one-dimensional free-congested Navier-Stokes equations. After a brief synthesis of the results obtained in [4] related to the existence and the asymptotic stability of partially congested profiles associated to the soft congestion Navier-Stokes system, we present a first local well-posedness result for the one-dimensional free-congested Navier-Stokes equations.
Enstrophy cascade in physical scales for the 3D Navier-Stokes equations
在物理上合理的流动假设下，在与边界条件无关的物理尺度上，Navier-斯托克斯方程显示出涡度拟能叶栅。
Liouville Theorem for 2D Navier-Stokes equations in Half Space
本文证明了半空间中二维Navier-斯托克斯方程的弱有界古解的Liouville定理。
Existence of Smooth Solutions of the Navier-Stokes Equations
本文证明了Navier-斯托克斯方程光滑解的存在性，从而对February man [3]提出的问题给出了肯定的回答.
Asymptotic behavior of solutions to 3D incompressible Navier-Stokes equations with damping
本文研究了在$\mathbb{R}^3$中含阻尼项$|u|^{β-1}u$（$β>1$）的Navier-斯托克斯方程和广义Navier-斯托克斯方程解的时间衰减率的上界.
2D Constrained Navier-Stokes Equations
研究了二维Navier-斯托克斯方程在解的$L^2$能量上的约束.利用不动点证明了约束Navier-斯托克斯方程在$\R^2$和$\T$上整体解的存在唯一性.我们还证明了当粘性$ν$为零时，约束Navier-Stokes方程的解收敛于欧拉方程的解。
Remark on Wolf's condition for boundary regularity of Navier-Stokes equations
我们证明了满足无滑移边界条件的Navier-斯托克斯方程解的Wolf正则性条件。
A global scheme for the incompressible Navier-Stokes equation on compact Riemannian manifolds
提出了紧致光滑黎曼流形上受控斯托克斯方程组的一个整体格式.
We are concerned with the global existence of classical solutions to the barotropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. We demonstrate that the classical solutions exists globally in time provided that the initial total energy is suitably small. It is worth noting that the initial density is allowed to have large oscillations and contain vacuum states. For our purpose, some new techniques and methods are adopted to obtain necessary a priori estimates, especially the estimates on the boundary. Moveover, we also give the …
Holder Continuity of Solutions of 2D Navier-Stokes Equations with Singular Forcing
讨论了二维不可压Navier-斯托克斯方程在奇异力作用下解的正则性。这个问题的动机是研究复杂的流体建模的Navier-斯托克斯方程耦合到一个非线性福克-普朗克方程描述嵌入在流体中的微观语料库。这自然导致有界附加应力，从而导致Navier-斯托克斯方程的$W^{-1,\infty}$强迫。
On the non-homogeneous Navier-Stokes system with Navier friction boundary conditions
讨论了具有Navier摩擦边界条件的非齐次Navier-Stokes方程组的弱解的存在性问题.当粘性趋于零时，我们还研究了具有Navier摩擦边界条件的非齐次Navier-Stokes方程组的弱解到变密度Euler方程的强解的收敛性，只要初值在$L^{2}$中收敛到足够光滑的极限.
Singular solutions of Navier Stokes equations with time-dependent external force terms in L2
证明了在L2空间中具有不定常外力的斯托克斯方程模型可以存在奇异解。
Stochastic homogenization for two dimensional Navier--Stokes equations with random coefficients
本文利用弱收敛与Stratonovich--Khasminskii平均原理，证明二维随机系数Navier--Stokes方程的解在分布上收敛到常系数方程的解，实现随机均匀化。
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