Related papers: An elementary approach to the pressureless Euler-N…
In this paper we prove nonexistence of stationary weak solutions to the Euler-Poisson equations and the Navier-Stokes-Poisson equations in $\Bbb R^N$, $N\geq 2$, under suitable assumptions of integrability for the density, velocity and the…
We study global well-posedness of strong solutions for the nonhomogeneous Navier-Stokes equations with density-dependent viscosity and initial density allowing vanish in $\mathbb{R}^2$. Applying a logarithmic interpolation inequality and…
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
The main objects of the present work are the quantum Navier-Stokes and quantum Euler systems; for the first one, in particular, we will consider constant viscosity coefficients. We deal with the concept of dissipative solutions, for which…
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 existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic…
We analyze the pressureless Navier-Stokes system with nonlocal attraction-repulsion forces. Such systems appear in the context of models of collective behavior. We prove the existence of weak solutions on the whole space $\mathbb{R}^3$ in…
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…
In this paper, we study the isothermal gas dynamics. We first establish the global existence of strong solutions to the one-dimensional isothermal Navier-Stokes system for smooth initial data without any smallness conditions, assuming that…
The Euler-Navier-Stokes (E-NS) system arises as a macroscopic description of kinetic-fluid interactions, derived from the local-Maxwellian closure of the Vlasov-Fokker-Planck-Navier-Stokes flow. In this paper, we investigate the singular…
This is the first of a series of papers devoted to the initial value problem for the Euler system of compressible fluids and augmented versions containing higher-order terms. We encompass solutions that have finite total energy and enjoy a…
We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the…
In 1995, Kazhikhov and Vaigant introduced a particular class of isentropic compressible Navier-Stokes equations with variable viscosity coefficients and, for the first time, established the existence of global smooth solutions for…
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…
Heuristic derivations of the Navier-Stokes equations are unable to reveal the applicability limits of these equations. In this paper we rederive the Navier-Stokes equations from kinetic theory, using a method that affords a step by step…
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…
The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution…
In this paper, we investigate the uniform regularity of solutions to the 3-dimensional isentropic compressible Navier-Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the…
This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space variables $t$ and $x$. The assumptions on the pressure…
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.…