On $L^1$ estimates of solutions of compressible viscoelastic system

Yusuke Ishigaki

On $L^1$ estimates of solutions of compressible viscoelastic system

Analysis of PDEs 2021-06-30 v1

Authors: Yusuke Ishigaki

Abstract

We consider the large time behavior of solutions of compressible viscoelastic system around a motionless state in a three-dimensional whole space. We show that if the initial preturbation belongs to $W^{2,1}$ , and is sufficiently small in $H^4\cap L^1$ , the solutions grow in time at the same rate as $t^{\frac{1}{2}}$ in $L^1$ due to diffusion wave phenomena of the system caused by interaction between sound wave, viscous diffusion and elastic wave.

Keywords

compressible viscoelastic system l1 estimate large time behavior diffusion wave three-dimensional whole space

Cite

@article{arxiv.2106.15266,
  title  = {On $L^1$ estimates of solutions of compressible viscoelastic system},
  author = {Yusuke Ishigaki},
  journal= {arXiv preprint arXiv:2106.15266},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:2005.01398

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