Flow of heat conducting fluid in a time-dependent domain

被引：0
作者：
Ondřej Kreml
Václav Mácha
Šárka Nečasová
Aneta Wróblewska-Kamińska
机构：
[1] Institute of Mathematics of the Academy of Sciences of the Czech Republic,Institute of Mathematics
[2] Polish Academy of Sciences,Department of Mathematics
[3] Imperial College London,undefined
来源：
Zeitschrift für angewandte Mathematik und Physik | 2018年 / 69卷
关键词：
Compressible Navier–Stokes–Fourier equations; Entropy inequality; Time-varying domain; Slip boundary conditions; 35Q35; 76N10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier–Stokes–Fourier system consisting of equation of continuity, momentum balance, entropy balance and energy equality. The velocity is supposed to fulfill the full-slip boundary condition and we assume that the fluid is thermally isolated. In the presented article we show the existence of a variational solution.
引用
收藏
相关论文
共 68 条
[1]  
Angot P(1999)A penalization method to take into account obstacles in incompressible viscous flows Numer. Math. 81 497-520
[2]  
Bruneau Ch-H(2007)The asymptotic problem for the springlike motion of a heavy piston in a viscous gas Q. Appl. Math. 65 471-498
[3]  
Fabrie P(2017)Dimension reduction for the full Navier–Stokes–Fourier system J. Math. Fluid Mech. 19 659-683
[4]  
Antman SS(2007)Navier’s slip and evolutionary Navier–Stokes-like systems with pressure and shear-rate dependent viscosity Indiana Univ. Math. J. 56 51-86
[5]  
Wilber JP(1989)Ordinary differential equations, transport theory and Sobolev spaces Invent. Math. 98 511-547
[6]  
Březina J(2004)On the motion of a viscous, compressible, and heat conducting fluid Indiana Univ. Math. J. 53 1707-1740
[7]  
Kreml O(2012)Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system J. Math. Fluid Mech. 14 717-730
[8]  
Mácha V(2011)Convergence of a Brinkman-type penalization for compressible fluid flows J. Differ. Equ. 250 596-606
[9]  
Bulíček M(2013)Weak solutions to the barotropic Navier–Stokes system with slip boundary conditions in time dependent domains J. Differ. Equ. 254 125-140
[10]  
Málek J(2012)Weak–strong uniqueness property for the full Navier–Stokes–Fourier system Arch. Ration. Mech. Anal. 204 683-706
1234567