Classical solutions for a generalized Euler equation in two dimensions (Q1378575)

The purpose of this paper is to give a new proof of global existence of smooth solutions for the initial value problem of two-dimensional Euler equations. First, local classical solutions are constructed as the limit of a Galerkin approximating sequence. Second, one proves a global a priori estimate in \(H^m\) which implies that the classical solutions are global. The key ingredient is a new \(L^p\) estimate on the nonlinear term.