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arxiv: 1610.00676 · v1 · pith:NGXVVVBTnew · submitted 2016-10-03 · 🧮 math.AP

Nonuniqueness of weak solutions to the SQG equation

Tristan Buckmaster , Steve Shkoller , Vlad Vicol This is my paper
classification 🧮 math.AP
keywords solutionsweakequationuniqueansweringarxivdissipationdissipative
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We prove that weak solutions of the inviscid SQG equations are not unique, thereby answering Open Problem 11 in the survey arXiv:1111.2700 by De Lellis and Sz\'ekelyhidi Jr. Moreover, we also show that weak solutions of the dissipative SQG equation are not unique, even if the fractional dissipation is stronger than the square root of the Laplacian.

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  1. Weak solutions of ideal MHD which do not conserve magnetic helicity

    math.AP 2019-07 unverdicted novelty 8.0

    Finite-energy weak solutions to ideal MHD exist with time-varying magnetic helicity, proving they are not attainable in the infinite-conductivity zero-viscosity limit.