Global Existence of Large DataWeak Solutions for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion  

作　　者：Yong Lu Milan Pokorny 

机构地区：[1]Department of Mathematics,Nanjing University,Nanjing,Jiangsu 210093,China [2]Charles University,Faculty of Mathematics and Physics,Sokolovsk´a 83,Prague 8,18675,Czech Republic

出　　处：《Analysis in Theory and Applications》2020年第3期348-372,共25页分析理论与应用（英文刊）

基　　金：The work of Y.Lu has been supported by the Recruitment Program of Global Experts of China.The work of M.Pokorny was supported by the grant of the Czech Science Foundation No.19-04243S.

摘　　要：We start with the compressible Oldroyd–B model derived in[2](J.W.Barrett,Y.Lu,and E.Suli,Existence of large-data finite-energy global weak solutions to a compressible Oldroyd–B model,Commun.Math.Sci.,15(2017),1265–1323),where the existence of global-in-time finite-energy weak solutions was shown in two dimensional setting with stress diffusion.In the paper,we investigate the case without stress diffusion.We first restrict ourselves to the corotational setting as in[28](P.L.Lions,and N.Masmoudi,Global solutions for some Oldroyd models of non-Newtonian flows,Chin.Ann.Math.,Ser.B,21(2)(2000),131–146)We further assume the extra stress tensor is a scalar matrix and we derive a simplified model which takes a similar form as the multi-component compressible Navier–Stokes equations,where,however,the pressure term related to the scalar extra stress tensor has the opposite sign.By employing the techniques developed in[30,35],we can still prove the global-in-time existence of finite energy weak solutions in two or three dimensions,without the presence of stress diffusion.

关 键 词：Compressible Oldroyd-B model stress diffusion weak solutions negative pressure term. 

分 类 号：O35[理学—流体力学] TP311.13[理学—力学] O175[自动化与计算机技术—计算机软件与理论]