Related papers: Lagrangian structure for two dimensional non-barot…
This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…
Fluids with shear-rate-dependent viscosity form a special class of non-Newtonian fluids that play a crucial role in continuum dynamics. We consider a compressible barotropic flow of such fluids, governed by a generalized Navier-Stokes…
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…
We consider a viscous compressible barotropic flow in the interval $[0,\pi]$ with homogeneous Dirichlet boundary conditions for the flow velocity and a constant rest state as initial data. Given two sufficiently close subintervals…
This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…
We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant…
We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in $\mathbb{R}^n.$ Different from the Navier-Stokes-Fourier system, the pressure is a nonlinear function of the density and…
We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure…
We study the 3-D compressible barotropic radiation fluid dynamics system describing the motion of the compressible rotating viscous fluid with gravitation and radiation confined to a straight layer. We show that weak solutions in the 3-D…
This paper addresses the issue of global existence of so-called $\kappa$-entropy solutions to the Navier-Stokes equations for viscous compressible and barotropic fluids with degenerate viscosities. We consider the three dimensional space…
This paper concerns the Cauchy problem of the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density. In particular, the initial density can have compact support. When the shear…
We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure $p(\varrho)=\varrho^\gamma$ for $\gamma\geq 9/5$ in three space dimension. The novelty of the paper is the approximation scheme…
The stationary Navier--Stokes--Cahn--Hilliard equations are considered, governing the motion of a compressible, two-phase fluid mixture with a diffuse interface. The free energy density in this paper has a singular logarithmic…
In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow or 3D case of non-stationary flow of incompressible fluid.…
We investigate the three dimensional compressible Navier-Stokes and the continuity equations in Cartesian coordinates for Newtonian fluids. The polytropic equation of sate is used as closing condition. The key idea is the three-dimensional…
We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
We introduce a two time-scale scheme which allows to extend the method of minimizing movements to hyperbolic problems. This method is used to show the existence of weak solutions to a fluid-structure interaction problem between a nonlinear,…
So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…
The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in $\mathbb{R}^2$. The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence…