Generalized flows and singular ODEs on differentiable manifolds

Abstract

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several existence and uniqueness results for solutions of such equations and flows of singular vector fields we compare the solution concept employed here with the purely distributional setting. Finally, we derive criteria securing that a sequence of smooth flows corresponding to a regularization of a given singular vector field converges to a measurable limiting flow.