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

This paper is dedicated to the global well-posedness issue of the compressible Oldroyd-B model in the whole space ${\mathbb{R}}^d$ with $d\ge 2$. 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.