On uniqueness for the critical wave equation

Nader Masmoudi (1) , Fabrice Planchon (2)

1 CIMS - Courant Institute of Mathematical Sciences [New York]
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: Equations aux dérivées partielles [math.AP]

Nader Masmoudi, Fabrice Planchon. On uniqueness for the critical wave equation. 2006. ⟨hal-00020030⟩