On Behavior of the Navier-Stokes Equations Beyond the Blow-Up Time and Local Anomalous Dissipation

Speaker: Professor Tobias Barker，University of Bath, UK          

Inviter: 张平

Title: On Behavior of the Navier-Stokes Equations Beyond the Blow-Up Time and Local Anomalous Dissipation

Language: English

Time & Venue: 2026.08.17   16:00-17:00   南楼N913

Abstract: In the first part, I will discuss results concerning absence of (interior) local anomalous dissipation in the 2D inviscid limit in the presence of boundaries. The implications for local balance laws for the limiting 2D Euler solution will also be discussed.  Joint work with  Milton C. Lopes Filho and Helena J. Nussenzveig Lopes  (Universidade Federal do Rio de Janeiro).In the second part, I will discuss quantitative classification of potentially singular 3D Navier-Stokes  solutions at any given time in the region of potential blow-up times. The quantitative lower bounds prior to any potential blow-up time (and in the open vicinity of it) are in principle amenable to numerical testing. Finally, I will discuss sufficient conditions for instantaneous blow-up to occur at a potential blow-up time (blow-up to the right).