Well-posedness in Critical Spaces for the Density-dependent Incompressible Viscoelastic Fluid System

Huazhao Xie; Yunxia Fu

Well-posedness in Critical Spaces for the Density-dependent Incompressible Viscoelastic Fluid System

Analysis of PDEs 2011-05-25 v1

Authors: Huazhao Xie , Yunxia Fu

Abstract

We are concerned with the well-posedness of the density-dependent incompressible viscoelastic fluid system. By Schauder-Tychonoff fixed point argument, when $\|{1}/{\rho_0}-1\|_{\dot{B}_{p,1}^{{N}/{p}}}$ is small, local well-posedness is showed to hold in Besov space. Furthermore, provided the initial data $(1/\rho_0 -1,\upsilon_0,U_0-I)$ is small under certain norm, we also get the existence of the global solution.

Keywords

density-dependent incompressible viscoelastic fluid well-posedness critical Besov space Schauder-Tychonoff fixed point global solution

Cite

@article{arxiv.1105.4690,
  title  = {Well-posedness in Critical Spaces for the Density-dependent Incompressible Viscoelastic Fluid System},
  author = {Huazhao Xie and Yunxia Fu},
  journal= {arXiv preprint arXiv:1105.4690},
  year   = {2011}
}

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