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SUMMARY:Revisit singularity formation for the inviscid primitive equations
  - Slim IBRAHIM (University of Victoria)
DTSTART:20220321T160000Z
DTEND:20220321T170000Z
UID:TALK171341@talks.cam.ac.uk
DESCRIPTION:The primitive equation is an important model for large scale f
 luid model including oceans and atmosphere. While solutions to the viscous
  model enjoy global regularity\, inviscid solutions may develop singularit
 ies in finite time. In this talk\, I will review the methods to show blowu
 p\, and share more recent progress on the qualitative properties of the si
 ngularity formation. Most notably\, I will provide a full description of t
 wo blowup mechanisms\, for a reduced PDE that is satisfied by a class of p
 articular solutions to the PEs. In the first one a shock forms\, and press
 ure effects are subleading\, but in a critical way: they localize the sing
 ularity closer and closer to the boundary near the blow-up time (with a lo
 garithmic in time law). This first mechanism involves a smooth blow-up pro
 file and is stable among smooth enough solutions. In the second one the pr
 essure effects are fully negligible\; this dynamics involves a two-paramet
 ers family of non-smooth profiles\, and is stable only by smoother perturb
 ations.\nThis is a joint work with C. Collot and Q. Lin.
LOCATION:Seminar Room 2\, Newton Institute
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