DOI: 10.1063/5.0350167 ISSN: 0022-2488
Asymptotic stability of the strong rarefaction wave for nonlinear viscoelastic model with non-Newtonian type viscosity under large initial perturbation
Hao Cheng, Wenchao Dong, Zhenhua GuoWe investigate the large-time asymptotic behavior of solutions to the Cauchy problem for a one-dimensional nonlinear viscoelastic model with non-Newtonian type viscosity (μ1 + μ2|ux|p−1)ux (p > 1, which represents a dilatant fluid) and a non-strictly convex stress function. By adopting an energy method and introducing a cutoff function for domain decomposition, we prove the stability of the strong rarefaction wave under large initial perturbation, without requiring the smallness of wave strength, provided that μ2 is sufficiently small. In particular, we not only establish the Lk-stability (k∈2,+∞) of the strong rarefaction wave, but also show that the non-Newtonian viscous term yields an Lp+1 decay property for spatial derivative.