scholarly journals INVISCID QUASI-NEUTRAL LIMIT OF A NAVIER-STOKES-POISSON-KORTEWEG SYSTEM

2018 ◽  
Vol 23 (2) ◽  
pp. 205-216
Author(s):  
Hongli Wang ◽  
Jianwei Yang
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Debye Length ◽  
Global Weak Solution ◽  
Viscosity Coefficient ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Dependent Viscosity ◽  
Cold Pressure ◽  
Incompressible Euler

The combined quasi-neutral and inviscid limit of the Navier-Stokes-Poisson-Korteweg system with density-dependent viscosity and cold pressure in the torus T3 is studied. It is shown that, for the well-prepared initial data, the global weak solution of the Navier-Stokes-Poisson-Korteweg system converges strongly to the strong solution of the incompressible Euler equations when the Debye length and the viscosity coefficient go to zero simultaneously. Furthermore, the rate of convergence is also obtained.

Existence of global weak solution for quantum Navier–Stokes system

2020 ◽  
Vol 31 (05) ◽  
pp. 2050038
Author(s):  
Jianwei Yang ◽  
Gaohui Peng ◽  
Huiyun Hao ◽  
Fengzhen Que
Keyword(s):  
Stokes System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Data ◽  
Global Weak Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Dependent Viscosity ◽  
Time Existence ◽  
Cold Pressure

In this paper, the barotropic compressible quantum Navier–Stokes equations with a density-dependent viscosity in a three-dimensional torus is studied. By introducing a cold pressure to handle the convection term, we prove the global-in-time existence of weak solutions to quantum Navier–Stokes equations for large data in the sense of standard definition.

scholarly journals One-dimensional compressible heat-conducting gas with temperature-dependent viscosity

2016 ◽  
Vol 26 (12) ◽  
pp. 2237-2275 ◽  
Author(s):  
Tao Wang ◽  
Huijiang Zhao
Keyword(s):  
Initial Data ◽  
Vacuum Solution ◽  
Viscosity Coefficient ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
One Dimensional ◽  
The One ◽  
Dependent Viscosity

We consider the one-dimensional compressible Navier–Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity [Formula: see text] and the heat conductivity [Formula: see text] depend on the specific volume [Formula: see text] and the temperature [Formula: see text] and are both proportional to [Formula: see text] for certain non-degenerate smooth function [Formula: see text]. We prove the existence and uniqueness of a global-in-time non-vacuum solution to its Cauchy problem under certain assumptions on the parameter [Formula: see text] and initial data, which imply that the initial data can be large if [Formula: see text] is sufficiently small. Such a result appears to be the first global existence result for general adiabatic exponent and large initial data when the viscosity coefficient depends on both the density and the temperature.

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

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