Fourier analysis of null forms and nonlinear wave equations

Abstract

The nonlinear terms of many equations, including wave maps and Yang-Mills have a special, "null", structure. In joint work with Sergiu Klainerman, the author uses techniques of Fourier analysis, such as generalizations and refinements of the restriction theorem applied to null forms to study the optimal Sobolev space in which such nonlinear wave equations are well posed.