The boundary integral method for the steady rotating Navier-Stokes equations in exterior domain (I): the existence of solution

In this paper, we apply the boundary integral method to the steady rotating Navier-Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and a infinite domain, we obtain a coupled problem by the steady rotating Navier-Stokes equations in finite domain and a boundary integral equation without using the artificial boundary condition. For the coupled problem, we show the existence of solution in a convex set.