Articles

FORMATION OF SINGULARITY FOR COMPRESSIBLE VISCOELASTICITY

  • Xianpeng Hu ,
  • Dehua Wang
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  • 1.Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA|2.Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received date: 2011-09-06

  Online published: 2012-01-20

Supported by

X. Hu’s research was supported in part by the National Science Foundation. D. Wang’s research was supported in part by the National Science Foundation and the Offce of Naval Research.

Abstract

The formation of singularity and breakdown of classical solutions to the three-dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu-tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.

Cite this article

Xianpeng Hu , Dehua Wang . FORMATION OF SINGULARITY FOR COMPRESSIBLE VISCOELASTICITY[J]. Acta mathematica scientia, Series B, 2012 , 32(1) : 109 -128 . DOI: 10.1016/S0252-9602(12)60007-1

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