相关论文: Optimal Time Decay of Navier-Stokes Equations With…
In this paper, we establish the space-time analyticity of global solutions to the incompressible Navier-Stokes equations with small initial data in critical \emph{Besov} spaces $\dot B^{3/p-1}_{p,q}$. Time decay rates of higher order…
In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible…
This paper is concerned with the Cauchy problem of the 3D compressible bipolar Navier--Stokes--Poisson (BNSP) system with unequal viscosities, and our main purpose is three--fold: First, under the assumption that $H^l\cap L^1$($l\geq…
Based on some elementary estimates for the space-time derivatives of the heat kernel, we use a bootstrapping approach to establish the optimal decay rates for the $L^q(\mathbb{R}^d)$ ($1\leq q\leq\infty$, $d\in\mathbb{N}$) norm of the…
In this paper, we investigate the convergence of the global large solution to its associated constant equilibrium state with an explicit decay rate for the compressible Navier-Stokes equations in three-dimensional whole space. Suppose the…
In this paper, we investigate the optimal decay rate for the higher order spatial derivative of global solution to the compressible Navier-Stokes (CNS) equations with or without potential force in three-dimensional whole space. First of…
We prove the existence of short time solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equation with low regularity initial data in Besov spaces $B^{r}_{p,q}(\mathbb{R}^n)$, $r>n/2p$. When $p=2$ and $n\geq 3$, we…
We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the…
We consider the large time behavior of the solution to the anisotropic Navier--Stokes equations in a $3$D half-space. Investigating the precise anisotropic nature of linearized solutions, we obtain the optimal decay estimates for the…
We are concerned with the construction of global-in-time strong solutions for the incompressible Vlasov-Navier-Stokes system in the whole three-dimensional space. One of our goals is to establish that small initial velocities with critical…
We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible…
We are concerned with the isentropic compressible Navier-Stokes system in the two-dimensional torus, with rough data and vacuum : the initial velocity is in the Sobolev space H^1 and the initial density is only bounded and nonnegative.…
We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…
This paper investigates the decay rates of the contact wave in one-dimensional Navier-Stokes equations. We study two cases of perturbations, with and without zero mass condition, i.e., the integration of initial perturbations is zero and…
We prove the existence of short time, low regularity solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equations with initial data in Sobolev spaces. In the special case of initial datum in the Sobolev space…
We study the regular sets of local energy solutions to the Navier-Stokes equations in terms of conditions on the initial data. It is shown that if a weighted $L^2$ norm of the initial data is finite, then all local energy solutions are…
The Navier-Stokes-Voigt equations are a regularization of the Navier-Stokes equations that share some of its asymptotic and statistical properties and have been used in direct numerical simulations of the latter. In this article we…
We study the initial-boundary value problem of the stochastic Navier--Stokes equations in the half space. We prove the existence of weak solutions in the standard Besov space valued random processes when the initial data belong to the…
The present paper is dedicated to the large time asymptotic behavior of global strong solutions near constant equilibrium (away from vacuum) to the compressible Navier-Stokes-Poisson equations. Precisely, we present that under the same…
We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly…