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Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain

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 Added by Charles Li
 Publication date 2018
  fields Physics
and research's language is English




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We consider the incompressible 2D Euler equations on bounded spatial domain $S$, and study the solution map on the Sobolev spaces $H^k(S)$ ($k > 2$). Through an elaborate geometric construction, we show that for any $T >0$, the time $T$ solution map $u_0 mapsto u(T)$ is nowhere locally uniformly continuous and nowhere Frechet differentiable.



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