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On the regularity of the solution map of the incompressible Euler equation (1302.0209v1)
Published 1 Feb 2013 in math.AP
Abstract: In this paper we consider the incompressible Euler equation on the Sobolev space $Hs(\Rn)$, $s > n/2+1$, and show that for any $T > 0$ its solution map $u_0 \mapsto u(T)$, mapping the initial value to the value at time $T$, is nowhere locally uniformly continuous and nowhere differentiable.