Sharp local well-posedness results for the nonlinear wave equation

Abstract

This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data.The new results obtained here are sharp in low dimension.In general, well-posedness involves existence, uniqueness and continuous dependence on the initial data.Naively, one would hope to have these properties hold for solutions in C(H s ) ∩ C 1 (H s-1 ), but it appears that there is little chance to establish uniqueness under this condition for the low values of s that we consider in this paper.Our definition of well-posedness thus includes

Locations

• Annals of Mathematics - View - PDF