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Karen Zaya: On Regularity Properties for Fluid Equations

Submitted by Andreas Freund on May 26, 2016 - 11:00am

Speaker: Karen Zaya, University of Illinois at Chicago

Date: May 26, 2016

Title: On Regularity Properties for Fluid Equations

Speaker: Fundamental mathematical questions about the 3D Navier-Stokes remain unanswered, such as the question of the regularity of solutions to the equations. Thus it is natural to ask: If we assume a smooth solution to the 3D Navier-Stokes equations $u$ loses regularity at time $T^*$, what is the rate of blow-up? In this talk, we discuss blow-up rates of solutions in the homogeneous Sobolev spaces. We will also discuss a newly developed regularity criterion for the 3D Boussinesq equations, which only imposes a condition on the low modes of the velocity $u$.