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

This work was partially supported by JSPS KAKENHI Grant Number 19J10056

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  • 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 data 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.

    Mathematics Subject Classification: Primary: 76N10, Secondary: 35B40, 35Q35, 76A10.


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