Asymptotic limits for strain-gradient viscoelasticity with nonconvex energy

Aseel AlNajjar; Stefano Spirito; Athanasios E. Tzavaras

doi:10.1088/1361-6544/add077

Asymptotic limits for strain-gradient viscoelasticity with nonconvex energy

Aseel AlNajjar^*, Stefano Spirito, Athanasios E. Tzavaras

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 ν → 0 or when the dispersion coefficient δ → 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 (1996 Commun. PDE 21 1771-79) on the rate of convergence of the zero-viscosity limit for the two-dimensional Navier-Stokes equations with bounded vorticity.

Original language	English (US)
Article number	055021
Journal	Nonlinearity
Volume	38
Issue number	5
DOIs	https://doi.org/10.1088/1361-6544/add077
State	Published - May 31 2025

Keywords

35G25
35Mxx
35Q74
74H20
74N20
asymptotic limits
hyperbolic-parabolic systems
strain-gradient theories
viscoelasticity

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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title = "Asymptotic limits for strain-gradient viscoelasticity with nonconvex energy",

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 ν → 0 or when the dispersion coefficient δ → 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 (1996 Commun. PDE 21 1771-79) on the rate of convergence of the zero-viscosity limit for the two-dimensional Navier-Stokes equations with bounded vorticity.",

keywords = "35G25, 35Mxx, 35Q74, 74H20, 74N20, asymptotic limits, hyperbolic-parabolic systems, strain-gradient theories, viscoelasticity",

author = "Aseel AlNajjar and Stefano Spirito and Tzavaras, {Athanasios E.}",

note = "Publisher Copyright: {\textcopyright} 2025 The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society.",

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doi = "10.1088/1361-6544/add077",

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T1 - Asymptotic limits for strain-gradient viscoelasticity with nonconvex energy

AU - AlNajjar, Aseel

AU - Spirito, Stefano

AU - Tzavaras, Athanasios E.

PY - 2025/5/31

Y1 - 2025/5/31

N2 - 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 → 0 or when the dispersion coefficient δ → 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 (1996 Commun. PDE 21 1771-79) on the rate of convergence of the zero-viscosity limit for the two-dimensional Navier-Stokes equations with bounded vorticity.

AB - 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 → 0 or when the dispersion coefficient δ → 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 (1996 Commun. PDE 21 1771-79) on the rate of convergence of the zero-viscosity limit for the two-dimensional Navier-Stokes equations with bounded vorticity.

KW - 35G25

KW - 35Mxx

KW - 35Q74

KW - 74H20

KW - 74N20

KW - asymptotic limits

KW - hyperbolic-parabolic systems

KW - strain-gradient theories

KW - viscoelasticity

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DO - 10.1088/1361-6544/add077

M3 - Article

AN - SCOPUS:105005155692

SN - 0951-7715

VL - 38

JO - Nonlinearity

JF - Nonlinearity

IS - 5

M1 - 055021

ER -

Asymptotic limits for strain-gradient viscoelasticity with nonconvex energy

Abstract

Keywords

ASJC Scopus subject areas

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