Special CRC1114 Colloquium Lecture: Please note the additional date 7.7.2023, 10:00 am, via Zoom-Meeting

Edriss Titi (location: WIAS) - Please note the additional date 7.7.2023, 10:00 am, via Zoom-Meeting:

https://us02web.zoom.us/j/85404222868?pwd=S3RMZFgxWTJXMzJVUmEzSEJrcjVtdz09

Title: The Inviscid Primitive Equations and the Effect of Fast Rotation

Large scale dynamics of the oceans and the atmosphere are governed by the primitive equation (PE).
It is well-known that the three-dimensional viscous PE is globally well-posed in Sobolev spaces. In
this talk, I will discuss the ill-posedness in Sobolev spaces, the local well-posedness in the space
of analytic functions, and the finite-time blowup of solutions to the three-dimensional inviscid PE
(also known as the hydrostatic Euler equations) with rotation (Coriolis force). Eventually, I will
also show, in the case of “well-prepared” analytic initial data, the regularizing effect of the Coriolis
force by providing a lower bound for the life-span of the solutions which grows toward infinity with
the rotation rate. The latter is achieved by a delicate analysis of a simple limit resonant system
whose solution approximates the corresponding solution of the 3D inviscid PE with the same initial
data. In addition, and if time allows I will discuss Onsager’s conjecture in the context of the inviscid
primitive equations.

Zoom-Meeting: https://us02web.zoom.us/j/85404222868?pwd=S3RMZFgxWTJXMzJVUmEzSEJrcjVtdz09

Meeting-ID: 854 0422 2868

Kenncode: 988186

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Meeting-ID: 854 0422 2868