Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy
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| Format: | Preprint |
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2024
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| author | AlNajjar, Aseel Spirito, Stefano Tzavaras, Athanasios E. |
| author_facet | AlNajjar, Aseel Spirito, Stefano Tzavaras, Athanasios E. |
| contents | 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 $ν\rightarrow 0$ or when the dispersion coefficient $δ\rightarrow 0$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_17115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy AlNajjar, Aseel Spirito, Stefano Tzavaras, Athanasios E. Analysis of PDEs 74H20, 74N20, 35Mxx, 35G25, 35Q74 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 $ν\rightarrow 0$ or when the dispersion coefficient $δ\rightarrow 0$. 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. |
| title | Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy |
| topic | Analysis of PDEs 74H20, 74N20, 35Mxx, 35G25, 35Q74 |
| url | https://arxiv.org/abs/2410.17115 |