相关论文: Strong Solution of Modified Anistropic 3D-Navier-S…
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…
In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the support of general meshes, possibly including polygonal or…
In two dimensions, we show existence of solutions to the stationary Navier Stokes equations on weighted spaces $\mathbf{H}^1_0(\omega,\Omega) \times L^2(\omega,\Omega)$, where the weight belongs to the Muckenhoupt class $A_2$. We show how…
In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of…
The chemotaxis-Navier-Stokes system \begin{equation*}\label{1} \left\{ \begin{array}{rcl} n_t+u\cdot\nabla n &=& \Delta \big(n c^{-\alpha} \big), \\[1mm] c_t+ u\cdot\nabla c &=& \Delta c -nc,\\[1mm] u_t + (u\cdot\nabla) u &=&\Delta u+\nabla…
We consider the inviscid limit of the stochastic damped 2D Navier- Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of…
In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…
In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow or 3D case of non-stationary flow of incompressible fluid.…
This paper presents an analytic solution of the incompressible Navier-Stokes equations as recurrence relations for the solution's derivatives, addressing the Clay Mathematics Institute's Millennium Prize problem on Navier-Stokes existence…
We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible…
We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It…
This paper examines the uniqueness/non-uniqueness of local-in-time strong solutions for the incompressible 3D Navier-Stokes equations in bounded domains, which are $\partial_t u=\nu \Delta u- u\cdot \nabla u-\nabla p+ f$ and $div~u=0$. The…
In this paper, by invoking the appropriate decomposition of pressure to exploit the energy hidden in pressure, we present some new $\varepsilon$-regularity criteria for suitable weak solutions of the 3D Navier-Stokes equations at one scale:…
A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in 3 dimensions with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations…
We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large.…
In this paper, we consider the solvability of the two-dimensional stationary Navier--Stokes equations on the whole plane $\mathbb{R}^2$. In [6], it was proved that the stationary Navier--Stokes equations on $\mathbb{R}^2$ is ill-posed for…
In this work we consider the generalized Navier-Stoke equations with the presence of a damping term in the momentum equation. % The problem studied here derives from the set of equations which govern the isothermal flow of incompressible,…
In this paper we study the deterministic homogenization problems for unsteady Navier-Stokes type equations, on one hand in an open set {\Omega} of R^{N}, on the other hand in porous media {\Omega}^{{\epsilon}}. In the second case, the…
We study a two-dimensional Navier--Stokes system with anisotropic viscosity, linear damping term, and an additive noise on the whole space $\mathbb{R}^2$. For this model we prove uniqueness of invariant measures when the damping coefficient…
In this paper, we derive decay rates for solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak solutions to these equations by refining the Fourier splitting…