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Nov 20, 2017 at 17:02 comment added Deane Yang It also appears to me that a contraction mapping argument using the solution operator for the linearized equation should work, too.
Nov 20, 2017 at 15:14 comment added Deane Yang The obvious thing to try is to solve the equation for a family of smooth initial data, converging to $\gamma$ and prove a priori estimates that imply that there exists a subsequence, which converges to a solution with initial data $\gamma$. The a priori estimates will probably imply uniqueness, too.
Nov 20, 2017 at 15:01 history edited Willie Wong
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Nov 20, 2017 at 8:56 history asked Matthias Ludewig CC BY-SA 3.0