AIMS Lab Seminar - Evan Miller - A Navier-Stokes regularity criterion involving control on the vorticity in a varying plane
Title: A Navier-Stokes regularity criterion involving control on the vorticity in a varying plane
Abstract: In 1999, Chae and Choe proved a scale critical regularity criterion for the Navier-Stokes equation on two components of the vorticity in what was the first scale-critical, component reduction type regularity criterion for the Navier-Stokes equation. In this talk, we will see that their result, which required control on the vorticity in a fixed plane, can be improved in the case $L^4_t L^2_x$ to a regularity criterion that allows the plane in which the vorticity is controlled to vary in space and time, so long as the gradient of the unit vector perpendicular to the plane remains bounded. Interestingly, this advance in regularity criteria in terms of vorticity comes not from the vorticity formulation of the Navier-Stokes regularity problem, but from the strain formulation. This regularity criterion also has some interesting implications related to the phenomenology of turbulence.
Date/Time: Monday December 7, 11:30am - 12:20pm
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Meeting ID: 910 5698 2661