Global Existence of Some Infinite Energy Solutions for a Perfect Incompressible Fluid

Abstract

This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we obtain an initial value problem for a nonlocal equation. We establish local well-posedness in all dimensions and persistence in time of these solutions for three and higher dimensions. We also examine a weaker class of global solutions.