On uniqueness for the critical wave equation

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.