Vanishing Shear Viscosity Limit and Incompressible Limit of Two Dimensional Compressible Dissipative Elastodynamics

Xianpeng Hu, Xiufang Cui

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

We study the vanishing shear viscosity limit and incompressible limit of
two dimensional compressible dissipative elastodynamics systems near the equilibrium. The large value of the volume viscosity forces the limit system to be incompressible, and the vanishing shear viscosity indicates that the limit system is inviscid. Due to the weak dispersive estimate in dimensions two and the lack of the null structures in non- linear terms, the generalised energy method (Klainerman and Sideris in Commun Pure Appl Math 49(3):615–666, 1996; Sideris in Ann Math 151(2):849–874, 2000; Sideris and Thomases in Commun Pure Appl Math 58(6):750–788, 2005), combined with the “ghost weight" method in (Alinhac in Invent Math 145(3):597–618, 2001), guarantees the global-in-time convergence from compressible dissipative elastodynamics to incom- pressible elastodynamics with the help of vector fields.
Original languageEnglish
Pages (from-to)3253-3336
Number of pages84
JournalCommunications in Mathematical Physics
Volume402
DOIs
Publication statusPublished - Jul 2023

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