Global Well-posedness of Incompressible Elastodynamics in Three Dimensional Thin Domain

TL;DR

This paper proves the global existence of classical solutions for incompressible isotropic elastodynamics in a three-dimensional thin domain with periodic boundary conditions, advancing understanding of elastodynamic behavior in constrained geometries.

Contribution

It establishes the global well-posedness of elastodynamics equations in a thin domain, a case previously not fully addressed in the literature.

Findings

Global existence of solutions proven for the model

Solutions remain regular for all time

Results applicable to thin elastic structures

Abstract

In this article, we prove global existence of classical solutions to the incompressible isotropic Hookean elastodynamics in three-dimensional thin domain $\Omega_\delta=\mathbb{R}^2\times [0,\delta]$ with periodic boundary condition.