Global solution in critical spaces to the compressible Oldroyd-B model with non-small coupling parameter

TL;DR

This paper proves the existence and uniqueness of global solutions for the compressible Oldroyd-B model in critical Besov spaces, even when the coupling parameter is not small, extending previous results.

Contribution

It extends prior work by establishing global well-posedness for the compressible Oldroyd-B model with non-small coupling parameters in critical spaces.

Findings

Global solutions exist for small initial data

Unique solutions are obtained in critical Besov spaces

Results apply to non-small coupling parameters

Abstract

This paper is dedicated to the global well-posedness issue of the compressible Oldroyd-B model in the whole space $\R^d$ with $d\ge2$. It is shown that this set of equations admits a unique global solution in a certain critical Besov space provided the initial data, but not necessarily the coupling parameter, is small enough. This result extends the work by Fang and the author [{J. Differential Equations}, {256}(2014), 2559--2602] to the non-small coupling parameter case.