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

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

2011-05-24

arxiv.org/abs/1105.4690v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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