Related papers: Exponential decay results for compressible viscous…
In this paper we give a new formulation of the compressible Navier-Stokes by introducing an suitable effective velocity $v=u+\n\va(\rho)$ provided that the viscosity coefficients verify the algebraic relation of \cite{BD}. We give in…
For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay…
We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the…
We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous ini- tial density. In dimension n = 2, 3, assuming only that the initial…
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…
In this paper, we study the global well-posedness of the 2D compressible Navier-Stokes equations with large initial data and vacuum. It is proved that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\l$ is the…
This paper is dedicated to the study of both viscous compressible barotropic fluids and Navier-Stokes equation with dependent density, when the viscosity coefficients are variable, in dimension $d\geq2$. We aim at proving the local and…
We discuss in this short note the local-in-time strong well-posedness of the compressible Navier-Stokes system for non-Newtonian fluids on the three dimensional torus. We show that the result established recently by Kalousek, M\'{a}cha, and…
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…
Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler…
We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a…
In this paper, we establish the global existence of small solutions to the inhomogeneous Navier-Stokes system in the half-space. The initial density only has to be bounded and close enough to a positive constant, and the initial velocity…
A fundamental open problem in the theory of the compressible Navier-Stokes equations is whether regular spherically symmetric flows can develop singularities, such as cavitation or implosion, in finite time. A formidable challenge lies in…
We establish the global existence of weak solutions to the isentropic compressible Navier-Stokes equations in three-dimensional annular cylinders with Navier-slip boundary conditions, allowing large axisymmetric initial data and vacuum…
The entropy is one of the fundamental states of a fluid and, in the viscous case, the equation that it satisfies is highly singular in the region close to the vacuum. In spite of its importance in the gas dynamics, the mathematical analyses…
In this work, we establish the global existence of strong solutions to the 2D and 3D compressible Navier-Stokes-Korteweg system with arbitrarily large initial data on the torus. This system was derived by Dunn and Serrin [Arch. Ration.…
In this paper, we show the incompressible and vanishing vertical viscosity limits for the strong solutions to the isentropic compressible Navier-Stokes system with anistropic dissipation, in a domain with Dirichlet boundary conditions in…
In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…
In this paper we study a vanishing pressure process for highly compressible Navier-Stokes equations as the Mach number tends to infinity. We first prove the global existence of weak solutions for the pressureless system in the framework…
We identify a class of measure-valued solutions of the barotropic Euler system on a general (un-bounded) spatial domain as a vanishing viscosity limit for the compressible Navier-Stokes system. Then we establish the weak…