文献类型：期刊文献

英文题名：Global existence in critical spaces for non Newtonian compressible viscoelastic flows

作者：Pan, Xinghong[1]; Xu, Jiang[1]; Zhu, Yi[2]

机构：[1] Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2019

外文期刊名：arXiv

收录：EI(收录号：20200288045)

语种：英文

外文关键词：Banach spaces - Deformation - Non Newtonian flow - Non Newtonian liquids - Rheology - Tensors - Viscoelasticity - Viscous flow

摘要：We are interested in the multi-dimentional compressible viscoelastic flows of Oldroyd type, which is one of non-Newtonian fluids exhibiting the elastic behavior. In order to capture the damping effect of the additional deformation tensor, to the best of our knowledge, the "div-curl" structural condition plays a key role in previous efforts. Our aim of this paper is to remove the structural condition and prove a global existence of strong solutions to compressible viscoelastic flows in critical spaces. The new ingredient lies in the introduction of effective flux (θ, G), which enables us to capture the dissipation arising from combination of density and deformation tensor. In absence of compatible conditions, the partial dissipation is found in non-Newtonian compressible fluids, which is weaker than that of usual Navier-Stokes equations.MSC Codes 35Q35 Copyright ? 2019, The Authors. All rights reserved.