Incompressible limit of a compressible Oldroyd-B model

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.