Global Solutions to Repulsive Hookean Elastodynamics

Xianpeng Hu, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

The global existence of classical solutions to the three dimensional repulsive Hookean elastodynamics around an equilibrium is considered. By linearization and Hodge’s decomposition, the compressible part of the velocity, the density, and the compressible part of the transpose of the deformation gradient satisfy Klein–Gordon equations with speed 2, while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one. The space-time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence.

Original languageEnglish (US)
Pages (from-to)543-590
Number of pages48
JournalArchive for Rational Mechanics and Analysis
Volume223
Issue number1
DOIs
StatePublished - Jan 1 2017

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ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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