EVENT DETAILS AND ABSTRACT

Title: Revisiting endpoint Serrin's criterion for the Navier-Stokes equation through profile decompositions
Speaker: Fabrice Planchon
Speaker Info: Paris Nord
Brief Description:
Special Note: Second talk of doubleheader
Abstract:

Recently, Escauriaza-Seregin-Sverak proved that for weak solutions to the incompressible Navier-Stokes equation, uniform (in time) boundedness of the spatial L3 norm prevents blow-up. We revisit this result in the framework of L3 mild solutions (à la Kato), following the Kenig-Merle roadmap for dispersive equations (extraction of a minimal blow-up solution through suitable profile decompositions, compactness at blow-up time and finally, like in E-S-S, backward uniqueness which precludes existence of such a critical solution). This is joint work with Isabelle Gallagher and Gabriel Koch.