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

[Moved Online] Introductory Workshop: Mathematical problems in fluid dynamics January 25, 2021 - February 05, 2021

January 28, 2021 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Vlad Vicol (New York University, Courant Institute)
Location: MSRI: Online/Virtual
Tags/Keywords
• Euler equation

• Shock

• Modulated Self-Similar Analysis

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Non-Conservative $H^{1/2-}$ Weak Solutions Of The Incompressible 3D Euler Equations

Abstract

For any positive regularity parameter $\beta < 1/2$, we construct infinitely many weak solutions of the 3D incompressible Euler equations on the periodic box, which lie in $C^0_t H^\beta_x$.

In particular, these solutions may be taken to have an $L^2$-based regularity index strictly larger than $1/3$, thus deviating from the scaling of the Kolmogorov-Obhukov $5/3$ power spectrum in the inertial range.

This is a joint work with T. Buckmaster, N. Masmoudi, and M. Novack.

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Non-Conservative $H^{1/2-}$ Weak Solutions Of The Incompressible 3D Euler Equations

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