Local Strong Solution to the Compressible Viscoelastic Fluid with Large Data

TL;DR

This paper proves the local existence and uniqueness of strong solutions with large initial data for 3D compressible viscoelastic fluids, using fixed-point theorems and weaker regularity assumptions.

Contribution

It establishes the first local strong solution result for compressible viscoelastic fluids with large data under weaker regularity conditions.

Findings

Existence and uniqueness of local strong solutions are proven.

The solution accommodates large initial data.

Weaker regularity than classical solutions is achieved.

Abstract

The existence and uniqueness of local in time strong solution with large initial data for the three-dimensional compressible viscoelastic fluid is established. The strong solution has weaker regularity than the classical solution. The Lax-Milgram theorem and the Schauder-Tychonoff fixed-point argument are applied.