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SUMMARY:Tobias Barker (École normale supérieure)
DTSTART:20200430T130000Z
DTEND:20200430T135000Z
DTSTAMP:20260423T021123Z
UID:IMS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/7/">Quan
 titative estimates for the Navier-Stokes equations via spatial concentrati
 on</a>\nby Tobias Barker (École normale supérieure) as part of PDE semin
 ar via Zoom\n\n\nAbstract\nIt remains open as to whether or not the 3D Nav
 ier-Stokes equations lose smoothness (`blow-up') in finite time. Starting 
 from Jean Leray\, many authors provided increasingly refined necessary con
 ditions for a finite-time blow-up to occur. The majority of these blow-up 
 behaviours are formulated in terms of critical or subcritical quantities\,
  which are notions relating to the scaling symmetry of the Navier-Stokes e
 quations. Very recently\, Tao used a new quantitative approach to infer th
 at certain 'slightly supercritical' quantities for the Navier-Stokes equat
 ions must become unbounded near a potential blow-up.\n\n\nIn this talk I'l
 l discuss a new strategy for proving quantitative bounds for the Navier-St
 okes equations\, as well as applications to  behaviours near a potential s
 ingularity . As a first application\, we prove a new potential blow-up rat
 e\, which is optimal for a certain class of potential non-zero backward di
 scretely self-similar solutions. As a second application\, we quantify a  
 conditional qualitative regularity result of Seregin (2012)\, which says t
 hat if the critical L_{3} norm of the velocity field is bounded along a se
 quence 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\, Univ
 ersité de Bordeaux).\n
LOCATION:https://researchseminars.org/talk/IMS/7/
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