Hs-global well-posedness for semilinear wave equations

Abstract

We consider the Cauchy problem for semilinear wave equations in R n with n⩾3. Making use of Bourgain's method in conjunction with the endpoint Strichartz estimates of Keel and Tao, we establish the H s -global well-posedness with s<1 of the Cauchy problem for the semilinear wave equation. In doing so a number of nonlinear a priori estimates is established in the framework of Besov spaces. Our method can be easily applied to the case with n=3 to recover the result of Kenig–Ponce–Vega.