Non-conservative H12− weak solutions of the incompressible 3D Euler equations

Tristan Buckmaster, Nader Masmoudi, Matthew Novack, Vlad Vicol

Research output: Working paperPreprint


For any positive regularity parameter $\beta < \frac 12$, we construct non-conservative weak solutions of the 3D incompressible Euler equations which lie in $H^{\beta}$ uniformly in time. In particular, we construct solutions which have an $L^2$-based regularity index \emph{strictly larger} than $\frac 13$, thus deviating from the $H^{\frac{1}{3}}$-regularity corresponding to the Kolmogorov-Obhukov $\frac 53$ power spectrum in the inertial range.
Original languageUndefined
StatePublished - Jan 22 2021


  • math.AP

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