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

TL;DR

This paper derives an explicit formula for infinite energy solutions to the 2D exterior div-curl problem with Dirichlet boundary conditions, addressing flow modeling with vorticity and divergence constraints.

Contribution

It provides the first explicit formula for solutions in the exterior 2D div-curl problem with Dirichlet boundary conditions, clarifying conditions for uniqueness.

Findings

Explicit formula for solutions derived

Relations between vorticity and divergence established

Conditions for uniqueness identified

Abstract

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.