Random attractors for the stochastic Navier--Stokes equations on the 2D unit sphere
Zdzislaw Brzeźniak, Beniamin Goldys, Quoc Thong Le Gia
本文证明了二维球面上Navier-斯托克斯方程在时空不规则随机强迫作用下随机吸引子的存在性。我们还推出了一个不变测度的存在性。
In this paper we prove the existence of random attractors for the Navier--Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce the existence of an invariant measure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The three-dimensional Navier-Stokes-$α$ model for fast rotating geophysical fluids is considered. The Navier-Stokes-$α$ model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian averaging and tend to the Navier-Stokes equations as $α\rightarrow 0^+$. We estimate upper bounds for the dimensions of global attractors and study the dependence of the dimensions on the parameter $α$. All the estimates are uniform in $α$, and our estimate of attractor dimensions remain finite when $α\rightarrow 0^+$.
Degenerate pullback attractors for the 3D Navier-Stokes equations
与前一篇文章一样，三维Navier-斯托克斯方程在边界力作用下也存在弱拉回吸引子。此外，这些吸引子由完整的有界轨迹组成。本文给出了拉回吸引子退化的一个充分条件。也就是说，如果Grashof常数足够小，拉回吸引子将是唯一的、完全的、有界的、强解上的一个点。然后，我们应用我们的结果提供了一个新的证明存在一个独特的，强大的，周期性的解决方案，三维Navier-Stokes方程与一个小的，周期性的强迫项。
This article covers the construction of exponential attractors in two different functional space settings; one is in Hilbert's space, and the other is in the Banach space. The former relies on the squeezing properties of solution trajectories, but the latter does not. We present these different methods for constructing exponential attractors using the three-dimensional Rotating Navier-Stokes-$α$ equations.
We consider the damped and driven Navier--Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain $Ω\subset\mathbf{R}^2$. We show that the damped Euler system has a (strong) global attractor in~$H^1(Ω)$. We also show that in the vanishing viscosity limit the global attractors of the Navier--Stokes system converge in the non-symmetric Hausdorff distance in $H^1(Ω)$ to the the strong global attractor of the limiting damped Euler system (whose solutions are not necessarily unique).
We give a comprehensive study of the 3D Navier-Stokes-Brinkman-Forchheimer equations in a bounded domain endowed with the Dirichlet boundary conditions and non-autonomous external forces. This study includes the questions related with the regularity of weak solutions, their dissipativity in higher energy spaces and the existence of the corresponding uniform attractors
Upper bounds for the attractor dimension of damped Navier-Stokes equations in $\mathbb R^2$
本文研究了平面上有阻尼和有驱动的二维Navier-斯托克斯方程的有限能量解，证明了相应的动力系统具有整体吸引子.当强迫项属于齐次索伯列夫空间的-1到1的全标度时，我们得到了它的分维的上界
We show that the Navier-Stokes as well as a random perturbation of this equation can be derived from a stochastic variational principle where the pressure is introduced as a Lagrange multiplier. Moreover we describe how to obtain corresponding constants of the motion.
Attractors for the Navier--Stokes--Voight equations and their dimension
研究 Navier--Stokes--Voight 方程吸引子维数，在三维给出改进的显式界，在二维证明正则化参数趋于零时估计收敛到 Navier--Stokes 系统结果。
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 whether zero is in the global attractor of the 2D Navier-Stokes equations
在Fréchet拓扑中，二维Navier-斯托克斯方程的全局吸引子中的零函数所对应的非零外力的集合是贫乏的.一个标准的泰勒展开在复杂的时间被用来描述在这个集合中的力。这导致了几个关系之间的某些Gevrey子类的$C^{\infty}$和一个新的上界的Gevrey规范的解决方案的吸引子，有效的带的时间分析。
Existence and invariant measure of pullback attractors for 3D Navier-Stokes-Voigt equations with delay
针对含时滞的三维非自治 NSV 方程，利用压缩函数方法证明拉回吸引子的存在性，并验证其正则性及唯一 Borel 不变概率测度族。
Attractor of the limiting Navier--Stokes--Voigt system in $\mathbb R^4$
本文研究四维全空间中Navier--Stokes--Voigt系统的吸引子理论，建立了适定性、耗散性、全局吸引子存在性及其维数估计，并指出该理论在四维时具有独特而简洁优美的特性。
We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the Caccioppoli's inequalities of the Stokes equations and the Navier-Stokes equations, in general, fail near boundary.
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.
Attractors for the Navier-Stokes-Cahn-Hilliard System with Chemotaxis and Singular Potential in 2D
本文研究二维带趋化性和奇异势的Navier-Stokes-Cahn-Hilliard系统，证明全局吸引子和指数吸引子的存在性，并推出全局吸引子具有有限分形维数。
In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes system with analytic data.
In this paper, we shall establish the global well-posedness, the space-time analyticity of the Navier-Stokes equations for a class of large periodic data $u_0 \in BMO^{-1}(\mathbb{R}^3)$. This improves the classical result of Koch \& Tataru \cite{koch-tataru}, for the global well-posedness with small initial data $u_0 \in BMO^{-1}(\mathbb{R}^n)$.
We study the stationary Stokes and Navier-Stokes equations with non-homogeneous Navier boundary condition in a bounded domain $Ω\subset\mathbb{R}^{3}$ of class $\mathcal{C}^{1,1}$. We prove existence, uniqueness of weak and strong solutions in $\mathbf{W}^{1,p}(Ω)$ and $\mathbf{W}^{2,p}(Ω)$ for all $1<p<\infty$ considering minimal regularity on the friction coefficient $α$. Moreover, we deduce uniform estimates on the solution with respect to $α$ which enables us to analyze the behavior of the solution when $α\rightarrow \infty$.
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.
In the note, a local regularity condition for axisymmetric solutions to the non-stationary 3D Navier-Stokes equations is proven. It reads that axially symmetric energy solutions to the Navier-Stokes equations have no Type I blowups.
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.
Attractors and their dimensions for the 3D Fractional Navier--Stokes--Voigt Equations
本文研究三维分数阶 Navier--Stokes--Voigt 方程，利用 Lieb--Thirring 和 Cwikel--Lieb--Rosenblum 谱不等式给出吸引子分形维数上界的改进估计，并将经典结果推广到分数阶情形。
In this paper, we provide a sufficient condition of the energy equality for the incompressible Navier-Stokes equations in bounded domains.
Fundamental solutions to the time-periodic Stokes and Oseen linearizations of the Navier-Stokes equations in dimension $n\geq 2$ are investigated. Integrability properties and pointwise estimates are established.
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。
In this paper, we justify the limit from the Navier-Stokes system in a thin domain to the hydrostatic Navier-Stokes/Prandtl system for the convex initial data with Gevrey 9/8 regualrity in $x$.
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.
In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{β-1}u$ ($β>1$) in $\mathbb{R}^3$.
We study 2D Navier-Stokes equations with a constraint on $L^2$ energy of the solution. We prove the existence and uniqueness of a global solution for the constrained Navier-Stokes equation on $\R^2$ and $\T$, by a fixed point argument. We also show that the solution of constrained Navier-Stokes converges to the solution of Euler equation as viscosity $ν$ vanishes.
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.
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。
Global and trajectory attractors for a nonlocal Cahn-Hilliard-Navier-Stokes system
Cahn-Hilliard-Navier-Stokes系统基于一个著名的扩散界面模型，描述了二元流体的不可压缩等温混合物的演化。一个非局部变量由Navier-斯托克斯方程与一个非局部Cahn-Hilliard方程适当耦合组成。作者与P. Colli一起证明了一类非局部Cahn-Hilliard-Navier-Stokes方程组在无滑移和无通量边界条件下整体弱解的存在性。即使在二维空间中，统一性仍然是一个悬而未决的问题。然而，在这种情况下，能量恒等式成立。这里利用这个属性来定义，继J.M. Ball方法，一个具有全局吸引子的广义半流。通过类似的论证，我们也可以证明具有给定速度场的对流非局部Cahn-Hilliard方程的（连通）整体吸引子的存在性，即使是在三维中。最后，我们证明了任何满足能量不等式的弱解也满足一个能量不等式。这使我们能够建立存在的轨迹吸引子也在三维不定常外力。
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.
It is shown that Navier Stokes equation models with time dependent external forces in L2 can have singular solutions.
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。
We prove in this paper a decay estimate for scaling invariant local energy solutions for some toy-models related to the incompressible Navier-Stokes system.
Global well-posedness for the two dimensional Navier-Stokes-Vlasov Equations
利用先验估计、特征线方法和半群分析方法，建立了二维不可压Navier-Stokes-Vlasov方程的整体适定性.
A Liouville type theorem is proven for the steady-state Navier-Stokes equations. It follows from the corresponding theorem on the Stokes equations with the drift. The drift is supposed to belong to a certain Morrey space.
In the note, a new regularity condition for axisymmetric solutions to the non-stationary 3D Navier-Stokes equations is proven. It is slightly supercritical.
Navier-Stokes equations: almost $L_{3,\infty}$-case
证明了Navier-斯托克斯方程解的正则性的一个充分条件。它推广了所谓的$L_{3,\infty}$情况。
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.
We extend Barker's weak-strong uniqueness results for the Navier--Stokes equations and consider a criterion involving Besov spaces and weighted Lebesgue spaces.
Liouville Type Theorem for Stationary Navier-Stokes Equations
证明了定常Navier-Stokes方程组在速度场整体属于$L_6$和$BM0^{-1}$的$R^3$中的光滑解必为零.
Existence and uniqueness of the global solution to the Navier-Stokes boundary problem
证明了Navier-Stokes边值问题弱解的整体存在唯一性.证明是简短的，基本上是独立的。
Forward Discretely Self-Similar Solutions of the Navier-Stokes Equations
推广了Jia和Sverak关于Navier-斯托克斯方程的自相似解的工作，我们证明了大的、向前的、离散的自相似解的存在性.
The Holder continuity of the swirl for the Navier-Stokes motions
应用DeGiorgi方法证明了Lq（0，T;Lp）（3/p+2/q < 1）的Navier-斯托克斯方程解的旋涡的Holder连续性。
Global regularity for the 3D Navier-Stokes and the 3D Euler equations
文章“3D Navier-Stokes和3D Euler方程的全局正则性”（arXiv：0711.2453）由于证明中的严重错误而被撤回。
We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the Navier-Stokes and Poisson equations, and blocking (vanishing normal flux) or selective (Dirichlet) boundary conditions for the ionic concentrations. We prove global existence and stability results for large data.
Uniform regularity for the Navier-Stokes equation with Navier boundary condition
证明了存在一个在粘性消失极限内一致的时间区间，且在该时间区间内，具有Navier边界条件的Navier-斯托克斯方程存在强解.该解在余正规索伯列夫空间中是一致有界的，并且只有一个正规导数在$L^\infty$中有界。这允许从强紧性论证得到不可压缩欧拉系统的消失粘性极限。
We characterise the pressure term in the incompressible 2D and 3D Navier-Stokes equations for solutions defined on the whole space.
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.
Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations
本文给出了三维Navier-Stokes方程组在任意正则初值下整体强解存在性的一个判别准则。
In this article, we study the solutions of the damped Navier--Stokes equation with Navier boundary condition in a bounded domain $Ω$ in $\mathbb{R}^3$ with smooth boundary. The existence of the solutions is global with the damped term $\vartheta |u|^{β-1}u, \vartheta >0.$ The regularity and uniqueness of solutions with Navier boundary condition is also studied. This extends the existing results in literature.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。