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On uniqueness for the critical wave equation

Nader Masmoudi·Fabrice Planchon
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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.

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Nader Masmoudi, Fabrice Planchon. 2006-03-03. On uniqueness for the critical wave equation. https://arxiv.org/abs/math/0603085

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