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Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain (1805.06507v2)
Published 16 May 2018 in math.AP, math-ph, math.DS, math.MP, nlin.CD, and physics.flu-dyn
Abstract: We consider the incompressible 2D Euler equations on bounded spatial domain $S$, and study the solution map on the Sobolev spaces $Hk(S)$ ($k > 2$). 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 Fr\'echet differentiable.