数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (1): 109-128.doi: 10.1016/S0252-9602(12)60007-1

• 论文 • 上一篇    下一篇

FORMATION OF SINGULARITY FOR COMPRESSIBLE VISCOELASTICITY

Xianpeng Hu, Dehua Wang   

  1. 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
  • 收稿日期:2011-09-06 出版日期:2012-01-20 发布日期:2012-01-20
  • 基金资助:

    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.

FORMATION OF SINGULARITY FOR COMPRESSIBLE VISCOELASTICITY

Xianpeng Hu, Dehua Wang   

  1. 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:2011-09-06 Online:2012-01-20 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.

摘要:

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.

关键词: compressible viscoelastic fluid, inviscid elasticity, local classical solution, formation of singularity, blowup, breakdown

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.

Key words: compressible viscoelastic fluid, inviscid elasticity, local classical solution, formation of singularity, blowup, breakdown

中图分类号: 

  • 35A05