Kinetic and Related Models (KRM)

Strong solutions to compressible barotropic viscoelastic flow with vacuum

Pages: 765 - 775, Volume 8, Issue 4, December 2015      doi:10.3934/krm.2015.8.765

       Abstract        References        Full Text (350.3K)       Related Articles       

Tong Tang - Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098, China (email)
Yongfu Wang - Department of Mathematics, Sichuan University, Chengdu, 610064, China (email)

Abstract: We consider strong solutions to compressible barotropic viscoelastic flow in a domain $\Omega\subset\mathbb{R}^{3}$ and prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Inspired by the work of Kato and Lax, we use the contraction mapping principle to get the result.

Keywords:  Existence, strong solutions, compressible viscoelastic flow.
Mathematics Subject Classification:  Primary: 35Q35, 76A10, 76N10.

Received: November 2014;      Revised: May 2015;      Available Online: July 2015.