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A sharp counterexample to local existence of low regularity solutions to Einstein's equations in wave coordinates

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If you have a question about this talk, please contact Prof. Mihalis Dafermos .

We give a sharp counter example to local existence of low regularity solutions to Einstein’s equations in wave coordinates. We show that there are initial data in H2 satisfying the wave coordinate condition such that there is no solution in H2 to Einstein’s equations in wave coordinates for any positive time. This result is sharp since Klainerman–Rodnianski and Smith–Tataru proved existence for the same equations with slightly more regular initial data.

This is joint work with Boris Ettinger.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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