Uniform Bound of the Highest Energy for the 3D Incompressible Elastodynamics

TL;DR

This paper investigates the long-term behavior of solutions to 3D incompressible elastodynamics, establishing bounds on the highest energy growth over time for small initial displacements.

Contribution

It provides a uniform bound on the energy growth of solutions, advancing understanding of the stability of 3D incompressible elastodynamics.

Findings

Established a uniform bound on the highest energy for solutions

Demonstrated stability of solutions with small initial displacements

Extended previous results to 3D incompressible elastodynamics

Abstract

This article concerns the time growth of Sobolev norms of classical solutions to the 3D incompressible isotropic elastodynamics with small initial displacements.