Communications in Mathematical Sciences

Volume 12 (2014)

Number 3

Blow-up criterion for compressible visco-elasticity equations in three dimensional space

Pages: 473 – 484

DOI: https://dx.doi.org/10.4310/CMS.2014.v12.n3.a4

Authors

Yi Du (Department of Mathematics, South China Normal University, Guangzhou, China)

Chun Liu (Department of Mathematics, Pennsylvania State University, State College, Penn., U.S.A.)

Qingtian Zhang (Department of Mathematics, Pennsylvania State University, State College, Penn., U.S.A.)

Abstract

In this paper, we prove a blow-up criterion for 3D compressible visco-elasticity in terms of the upper bound of the density and the deformation tensor. Due to the special structure of the equation, we get the cancellation to the derivatives of the density and transform tensor, which brings us the desired results.

Keywords

3D visco-elasticity, compressible, blow-up criterion

2010 Mathematics Subject Classification

35Q35, 76A10

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Published 26 November 2013