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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Revisit singularity formation for the inviscid primitive equations

## Revisit singularity formation for the inviscid primitive equationsAdd to your list(s) Download to your calendar using vCal - Slim IBRAHIM (University of Victoria)
- Monday 21 March 2022, 16:00-17:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. TUR - Mathematical aspects of turbulence: where do we stand? The primitive equation is an important model for large scale fluid model including oceans and atmosphere. While solutions to the viscous model enjoy global regularity, inviscid solutions may develop singularities in finite time. In this talk, I will review the methods to show blowup, and share more recent progress on the qualitative properties of the singularity formation. Most notably, I will provide a full description of two blowup mechanisms, for a reduced PDE that is satisfied by a class of particular solutions to the PEs. In the first one a shock forms, and pressure effects are subleading, but in a critical way: they localize the singularity closer and closer to the boundary near the blow-up time (with a logarithmic in time law). This first mechanism involves a smooth blow-up profile and is stable among smooth enough solutions. In the second one the pressure effects are fully negligible; this dynamics involves a two-parameters family of non-smooth profiles, and is stable only by smoother perturbations. This is a joint work with C. Collot and Q. Lin. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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