On uniqueness for the critical wave equation

Details On uniqueness for the critical wave equation On uniqueness for the critical wave equation

2006-03-03

arxiv.org/abs/math/0603085v1

Mathematics

Analysis of PDEs

12 pages, to appear in Comm. Partial Differential Equations

Scientific paper

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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