On the hydrostatic approximation of 3D Oldroyd-B model

Abstract

In this paper, we study the hydrostatic approximation for the 3D Oldroyd-B model. Firstly, we derive the hydrostatic approximate system for this model and prove the global well-posedness of the limit system with small analytic initial data in horizontal variable. Then we justify the hydrostatic limit strictly from the re-scaled Oldroyd-B model to the hydrostatic Oldroyd-B model and obtain the precise convergence rate.