On uniqueness for the critical wave equation

Abstract

We prove the uniqueness of weak solutions to the critical defocusing wave equation in 3D under a local energy inequality condition. More precisely, we prove the uniqueness of $u\in L^{\infty }\_t({\dot{H}}^1)\cap {\dot{W}}^{1,\infty }\_t(L^2)$, under the condition that $u$ verifies some local energy inequalities.

12 pages, to appear in Comm. Partial Differential Equations