Incompressible limit of a compressible Oldroyd-B model

TL;DR

This paper establishes the global existence of solutions for a 3D compressible Oldroyd-B model under small initial data and rigorously justifies the transition to the incompressible model in the limit.

Contribution

It provides the first rigorous derivation of the incompressible limit for the compressible Oldroyd-B model in three dimensions.

Findings

Global well-posedness of strong solutions under small initial data

Uniform regularity in the incompressible limit

Rigorous justification of the incompressible limit transition

Abstract

In this paper, we consider the Cauchy problem for a compressible Oldroyd-B model in three dimensions. Under some smallness assumptions on the initial data, we obtain the global wellposedness of strong solution with uniform regularity. Moreover, we provide a rigorous justification for the link between the compressible model and the corresponding incompressible model via incompressible limits.