Related papers: Global classical solutions to a Compressible Model…
This paper is concerned with a fluid-particle system given by the incompressible Navier-Stokes equations coupled with the Vlasov(-Fokker-Planck) equation through a drag force. Such a model arises naturally in the study of aerosols, sprays,…
We investigate the inertial limit of the compressible Navier--Stokes system posed on the $3$-dimensional torus, and allowing for regions of vacuum. Considering global-in-time finite-energy weak solutions of a scaled system, we rigorously…
In this paper, we study a hyperbolic version of the Navier-Stokes equations, obtained by using the approximation by relaxation of the Euler system, evolving in a thin strip domain. The formal limit of these equations is a hyperbolic Prandtl…
We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscousities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric…
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…
We introduce a new phase field model for binary mixtures of incompressible micropolar fluids, which are among the simplest categories of fluids exhibiting internal rotations. The model fulfils local and global dissipation inequalities so…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…
This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those…
In this paper we study the convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a highly regular unique strong solution and analyse its global…
This article delves into the micro-macro modeling of polymeric fluids, considering various microscopic potential energies, including the classical Hookean potential, as well as newly proposed modified Morse and Elastic-plastic potentials.…
We prove global in time existence of solutions of the Euler compressible equations for a Van der Waals gas when the density is small enough in $\H{m}$, for $m$ large enough. To do so, we introduce a specific symmetrisation allowing areas of…
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 consider global in time solutions of the Navier-Stokes-Fourier system describing the motion of a general compressible, viscous and heat conducting fluid far from equilibirum. Using a new concept of weak solution suitable to accommodate…
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…
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic…
We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…
We construct a unique local strong solution to the finitely extensible nonlinear elastic (FENE) dumbbell model of Warner-type for an incompressible polymer fluid (described by the Navier-Stokes-Fokker-Planck equations) interacting with a…
A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…
The grand potential for open systems describes thermodynamics of fluid flows at low Mach numbers. A new system of reduced equations for the grand potential and the fluid momentum is derived from the compressible Navier-Stokes equations. The…
We study the Navier--Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical…