For every θ<1/3, in a natural space of C^θ weak solutions of Euler, a residual set has kinetic energy in C^{2θ/(1-θ)} but in no better fractional Sobolev class, and smooth solutions are nowhere dense.
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Sharp energy regularity and typicality results for H\"older solutions of incompressible Euler equations
For every θ<1/3, in a natural space of C^θ weak solutions of Euler, a residual set has kinetic energy in C^{2θ/(1-θ)} but in no better fractional Sobolev class, and smooth solutions are nowhere dense.