Related papers: On the motion of three-dimensional compressible is…
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.…
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…
We are concerned with the global existence and vanishing dispersion limit of strong/classical solutions to the Cauchy problem of the one-dimensional barotropic compressible quantum Navier-Stokes equations, which consists of the compressible…
We prove the existence of weak solutions to the steady compressible Navier-Stokes system in the barotropic case for a class of pressure laws singular at vacuum. We consider the problem in a bounded domain in R^2 with slip boundary…
This work is devoted to study the global existence of strong and classical solutions to compressible Navier-Stokes equations with or without density jump on the moving boundary for spherically symmetric motion. We establish a unified method…
The inhomogeneous incompressible Navier-Stokes equations with fractional Laplacian dissipations in the multi-dimensional whole space are considered. The existence and uniqueness of global strong solution with vacuum are established for…
We consider the 3D isentropic compressible Navier-Stokes equations with degenerate viscousities and vacuum. The degenerate viscosities $\mu(\rho)$ and $\lambda(\rho)$ are proportional to some power of density, while the powers of density in…
This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data…
We investigate the barotropic compressible Navier-Stokes equations with the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density that is allowed to vanish, we establish the global…
We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic…
We study a modified three-dimensional incompressible anisotropic Navier-Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a…
We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of data allowing growth at spatial infinity. Namely, we show the global existence of suitable weak solutions when the initial data…
In the spirit of D. Hoff's weak solution theory for the compressible Navier-Stokes equations (CNS) with bounded density, in this paper we establish the global existence and regularity properties of finite-energy weak solutions to an initial…
This paper concerns the isentropic compressible Navier-Stokes equations in a three-dimensional (3D) bounded domain with slip boundary conditions and vacuum. It is shown that the classical solutions to the initial-boundary-value problem of…
In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…
This paper is concerned with the three-dimensional equations of a simplified hydrodynamic flow modeling the motion of compressible, nematic liquid crystal materials. The authors establish the global existence of classical solution to the…
In this paper, we consider the three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity in presence of vacuum over bounded domains. Global-in-time unique strong solution is proved to exist when $\|\nabla…