Convergence rates of solutions to the compressible Hookean elastodynamics

Xiao Wang, Hao Xu, Xin Xu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the low Mach number limit of the compressible Hookean elastodynamics in a bounded domain. Based on previous uniform existence and convergence results, we further study the convergence rates of the solutions. By combining time-average method and the energy estimates, we show that, as the Mach number ϵ goes to zero, the solutions of the compressible Hookean elastodynamics will converge to the solution of the limit system at the rate of O(ϵ) when the initial data are ill-prepared. If the initial data are assumed to be well-prepared, the convergence rates can be improved to O(ϵ2).

Original languageEnglish
Article number224
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume73
Issue number6
DOIs
StatePublished - Dec 2022
Externally publishedYes

Keywords

  • Convergence rates
  • Hookean elastodynamics
  • Mach number

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