A note on the existence and uniqueness of plane steady viscous flow in exterior domains

Abstract

In this article we study the existence and uniqueness of solutions of the stationary Navier–Stokes equations in two‐dimensional exterior domains. Using well‐known L^q‐estimates for the Oseen problems and an iterative process based on repeated resolution of Oseen problems, we prove the existence and uniqueness of solutions of the Navier–Stokes equations in two‐dimensional exterior domains. Our results give another answer to a question recently raised in [2,3] concerning the summability with exponent p∈(1,2) of the gradient of the velocity of stationary plane flow of a viscous fluid in exterior domains.