Long-time existence of nonlinear inhomogeneous compressible elastic waves

TL;DR

This paper proves almost global and global existence results for nonlinear inhomogeneous compressible elastic waves in three dimensions, extending previous homogeneous case results to inhomogeneous media with small density disturbances.

Contribution

It establishes the first almost global and global existence results for inhomogeneous elastic waves, generalizing prior homogeneous case theories.

Findings

Almost global existence in inhomogeneous case

Global existence in inhomogeneous case

Extension of homogeneous results to inhomogeneous media

Abstract

In this paper, we consider the nonlinear inhomogeneous compressible elastic waves in three spatial dimensions when the density is a small disturbance around a constant state. In homogeneous case, the almost global existence was established by Klainerman-Sideris [1996_CPAM], and global existence was built by Agemi [2000_Invent. Math.] and Sideris [1996_Invent. Math., 2000_Ann. Math.] independently. Here we establish the corresponding almost global and global existence theory in the inhomogeneous case.