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arXiv · 2410.17115

Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy

Aseel AlNajjar·Stefano Spirito·Athanasios E. Tzavaras
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Abstract

We consider the system of viscoelasticity with higher-order gradients and nonconvex energy in several space dimensions. We establish the asymptotic limits when the viscosity $\nu\rightarrow 0$ or when the dispersion coefficient $\delta \rightarrow 0$. For the latter problem, it is worth noting that, for the case of two space dimensions, we also establish a rate of convergence. This result bears analogies to a result of Chemin \cite{jean1996remark} on the rate of convergence of the zero-viscosity limit for the two-dimensional Navier-Stokes equations with bounded vorticity.

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Aseel AlNajjar, Stefano Spirito, Athanasios E. Tzavaras. 2024-10-22. Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy. https://arxiv.org/abs/2410.17115

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