# On uniqueness for the critical wave equation

Research paper by Nader Masmoudi, Fabrice Planchon

Indexed on: 03 Mar '06Published on: 03 Mar '06Published in: Mathematics - Analysis of PDEs

#### 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.