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On the well-posedness of the incompressible Euler Equation (1301.5997v1)
Published 25 Jan 2013 in math.AP
Abstract: In this thesis we prove that the homogeneous incompressible Euler equation of hydrodynamics on the Sobolev spaces $Hs(\Rn)$, $n \geq 2$ and $s > n/2+1$, can be expressed as a geodesic equation on an infinite dimensional manifold. As an application of this geometric formulation we prove that the solution map of the incompressible Euler equation, associating intial data in $Hs(\Rn)$ to the corresponding solution at time $t > 0$, is nowhere locally uniformly continuous and nowhere differentiable.