Global well-posedness for the hydrostatic Oldroyd-B model

Abstract

The Oldroyd-B model plays an important role in the viscoelastic flows. In this paper, we study the Oldroyd-B model in a strip domain $R\times T$. We first derive the hydrostatic approximate system for the Oldroyd-B model and then we prove the global well-posedness of this limit system with small analytic data in horizontal variable. Finally, we justify the limit from the re-scaled Oldroyd-B model to the hydrostatic Oldroyd-B model.