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

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

Start:

Monday, October 9, 2023 12:00 pm

End:

Monday, October 9, 2023 12:50 pm

Location:

PHAR 107

Patrick Phelps

Temple University

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.

Contact:

Elaine Cozzi