An elementary proof of global or almost global existence for quasi-linear wave equations
This paper gives a detailed outline on the energy integral method for proving global and almost global existence of solutions of nonlinear wave equations, methods which were developed mainly by Klainerman and Sideris. The main purpose of the author is to avoid the use of Lorentz boosts, and of direct estimates of fundamental solutions. The main result is an almost global existence theorem for solutions of quasilinear \(3+1\) dimensional wave equatons, together with an explicit estimate of the life span of solutions depending exponentially on the smallness parameter of the initial data; smallness is measured in generalized energies. The proof uses Sobolev type estimates introduced by Sideris, Hidano, and Nakanishi, which are applied in the proof of the main weighted state space estimates of Klainerman and Sideris, and in the proof of the energy estimates.
scientific article; zbMATH DE number 2114246
scientific article