Global Solutions to Repulsive Hookean Elastodynamics

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

4 Scopus Citations
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Original languageEnglish
Pages (from-to)543-590
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume223
Issue number1
Publication statusPublished - 1 Jan 2017

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.