Explicit Formula of the Infinite Energy Solutions for the Exterior 2D Div-Curl Problem with Dirichlet Boundary Condition

In the paper we study the 2D div-curl problem in the exterior domain which models the flow with given vorticity, divergency, boundary condition at infinity, and Dirichlet condition on the solid surface. We will find the relations on vorticity and divergence for uniqueness solvability of the problem and deduce the explicit formula.