A blow-up criterion for 3-D compressible visco-elasticity

TL;DR

This paper establishes a criterion for the blow-up of solutions in 3D compressible visco-elasticity based on bounds of density and deformation tensors, utilizing structural cancellations in derivatives.

Contribution

It introduces a new blow-up criterion linked to the upper bounds of key physical quantities in 3D compressible visco-elasticity, leveraging structural properties of the deformation tensor.

Findings

Blow-up occurs when density or deformation tensor bounds are exceeded.

Structural cancellations in derivatives are crucial for the analysis.

The criterion provides conditions to predict solution blow-up.

Abstract

In this paper, we shall prove a blow-up criteria in terms of the upper bound of the density, deformation tensor and the gradient of deformation tensor for 3D compressible visco-elasticity. Based on the structure of deformation tensor, we find a cancelation in higher order derivatives, which brings us the desired results.