Global low regularity solutions for nonlinear elastic waves

TL;DR

This paper proves the global existence of low regularity solutions for 3-D nonlinear elastic waves satisfying the null condition, focusing on radially symmetric cases with small initial data.

Contribution

It establishes global solutions under low regularity initial data for nonlinear elastic waves, a significant extension beyond classical regularity requirements.

Findings

Global existence of solutions for small data in $H^3\times H^2$

Results specific to radially symmetric cases

Solutions exist with low regularity initial data

Abstract

We study the Cauchy problem for 3-D nonlinear elastic waves satisfying the null condition with low regularity initial data. In the radially symmetric case, we prove the global existence of a low regularity solution for every small data in $H^3\times H^2$ with a low weight.