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arXiv · 2106.15266

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

Yusuke Ishigaki
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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.

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Yusuke Ishigaki. 2021-06-29. On $L^1$ estimates of solutions of compressible viscoelastic system. https://arxiv.org/abs/2106.15266

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