Non-conservative $H^{\frac{1}{2}-}$ weak solutions of the incompressible 3D Euler equations

Abstract

For any positive regularity parameter $\beta <\frac{1}{2}$, 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 $\frac{1}{3}$, thus deviating from the $H^{\frac{1}{3}}$-regularity corresponding to the Kolmogorov-Obhukov $\frac{5}{3}$ power spectrum in the inertial range.

155 pages, 11 figures, typos corrected

References in corpus (4)

• The multifractal nature of turbulent energy dissipation
• Sharp nonuniqueness for the Navier-Stokes equations
• Positive solutions of transport equations and classical nonuniqueness of characteristic curves
• On Non-uniqueness of Hölder continuous globally dissipative Euler flows