Asymptotic properties and separation rates for local energy solutions to the Navier-Stokes equations

Analysis Seminar

Thursday, November 2, 2023 - 3:30pm to 4:30pm

Patrick M. Phelps

Department of Mathematics

Location

Temple University

DRL 3C2

We present recent results on spatial decay and properties of non-uniqueness for the 3D Navier-Stokes equations. We show asymptotics for the ‘non-linear’ part of scaling invariant flows with data in subcritical classes. Motivated by recent work on non-uniqueness, we investigate how non-uniqueness of the velocity field would evolve in time in the local energy class. Specifically, by extending our subcritical asymptotics to approximations by Picard iterates, we may bound the rate at which two solutions, evolving from the same data, may separate pointwise. We conclude by extending this separation rate to solutions with no scaling assumption. Joint work with Zachary Bradshaw.

April

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How to get to Penn's Mathematics Department

The Mathematics Department Office is located on the fourth (top) floor of David Rittenhouse Laboratory ("DRL"). The building is at 209 South 33rd Street (the Southeast corner of 33rd. and Walnut Streets). Note 33rd Street runs one way north while Walnut runs one way west.

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