Related papers: About the barotropic compressible quantum Navier-S…
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a…
We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains…
The construction of weak solutions to compressible Navier-Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in…
We study the global existence and uniqueness of classical solutions to the three-dimensional compressible isentropic Navier-Stokes equations with vacuum and external potential forces which could be arbitrarily large provided the initial…
Here we investigate the Cauchy problem for the barotropic Navier-Stokes equations in R^n, in the critical Besov spaces setting. We improve recent results as regards the uniqueness condition: initial velocities in critical Besov spaces with…
In this paper, we consider the global spherically symmetric strong solutions to the compressible Navier-Stokes equations with far-field vacuum and density-dependent degenerate viscosity, following the framework proposed by Bresch-Vasseur-Yu…
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…
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…
In this paper we consider the Quantum Navier-Stokes system both in two and in three space dimensions and prove global existence of finite energy weak solutions for large initial data. In particular, the notion of weak solutions is the…
We investigate the barotropic compressible Navier-Stokes equations with slip boundary conditions in a three-dimensional (3D) simply connected bounded domain, whose smooth boundary has a finite number of two-dimensional connected components.…
We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong…
We consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by time periodic inflow/outflow boundary conditions. We show that the problem admits a time periodic…
We consider the Quantum Navier-Stokes system in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. The main novelties are that vacuum regions are included in the weak formulation and no…
The present article studies solutions to the compressible Navier-Stokes equations for ideal gases in one dimension when thermal conductivity is present but very weak, while viscosity is positive and constant. The main novelty is the…
The compressible Navier-Stokes system with the constant viscosity and the nonlinear heat conductivity which is proportional to a positive power of the temperature and may be degenerate is considered. Under the outer pressure boundary…
In my PhD thesis I show the existence of global-in-time weak solutions for a Navier-Stokes fluid interacting with a linearly elastic shell of Koiter type. This is achieved by the introduction of a new method for showing the compactness of…
The purpose of this paper is to study the vanishing viscosity limit for the d-dimensional Navier--Stokes equations in the whole space: \begin{equation*} \begin{cases} \partial_tu^\varepsilon+u^\varepsilon\cdot \nabla…
We prove that weak solutions to the compressible Navier-Stokes equations satisfy the energy equality under a Shinbrot-type regularity criterion. Our method applies to the fluids with both constant and degenerate viscosity and relies on a…
Global existence of solutions to the compressible Navier-Stokes-Korteweg system around a constant state is studied. This system describes liquid-vapor two phase flow with phase transition as diffuse interface model. In previous works they…
The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak…