Steady States in Hydrodynamics

Abstract

The purpose of this work is to understand the topological structures of the steady states of 2D incompressible Euler equation. In particular, we are interested in the rigidity and flexibity aspects of steady states.In the rigidity aspects, we want to study the topological behavior of the steady states in certain fine topologies. In the flexibility part, we want to construct certain steady states with distinct topological features near a given steady state. Our ultimate goal is to understand the global behavior of solutions of 2D incompressible Euler equations through steady states.