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Analysis Seminar

Wednesday, May 1, 2024
3:00pm to 4:00pm
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Linde Hall 187
Critical non-uniqueness in a shell model of the Navier-Stokes equations
Stan Palasek, Department of Mathematics, IAS/Princeton,

An outstanding question of the theory of the incompressible Navier-Stokes equations is whether solutions are unique in the Leray class, i.e., the weak solutions that dissipate energy. There is compelling numerical evidence due to Jia and Sverak of a reflection symmetry-breaking phenomenon leading to non-uniquness. In this talk we propose a new non-uniqueness scenario based on breaking of the (discrete) scaling symmetry, demonstrated in a shell model of the Navier-Stokes equations first formulated by Obukhov. We construct data in a critical space that gives rise to distinct Leray solutions which are approximately self-similar and ``smooth'' (in the sense of exponentially decaying energy spectrum) for positive times.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit https://ucla.zoom.us/j/9264073849.