BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tobias Barker (École normale supérieure) DTSTART:20200430T130000Z DTEND:20200430T135000Z DTSTAMP:20260404T143402Z UID:IMS/7 DESCRIPTION:Title: Quantitative estimates for the Navier-Stokes equations via spatial conc entration\nby Tobias Barker (École normale supérieure) as part of PD E seminar via Zoom\n\n\nAbstract\nIt remains open as to whether or not the 3D Navier-Stokes equations lose smoothness (`blow-up') in finite time. St arting from Jean Leray\, many authors provided increasingly refined necess ary conditions for a finite-time blow-up to occur. The majority of these b low-up behaviours are formulated in terms of critical or subcritical quant ities\, which are notions relating to the scaling symmetry of the Navier-S tokes equations. Very recently\, Tao used a new quantitative approach to i nfer that certain 'slightly supercritical' quantities for the Navier-Stoke s equations must become unbounded near a potential blow-up.\n\n\nIn this t alk I'll discuss a new strategy for proving quantitative bounds for the Na vier-Stokes equations\, as well as applications to behaviours near a pote ntial singularity . As a first application\, we prove a new potential blow -up rate\, which is optimal for a certain class of potential non-zero back ward discretely self-similar solutions. As a second application\, we quant ify a conditional qualitative regularity result of Seregin (2012)\, which says that if the critical L_{3} norm of the velocity field is bounded alo ng a sequence of times tending to time $T$ then no blow-up occurs at time $T$.\n\n\nThis talk is based upon joint work with Christophe Prange (CNRS \, Université de Bordeaux).\n LOCATION:https://stable.researchseminars.org/talk/IMS/7/ END:VEVENT END:VCALENDAR