The mathematical analysis of the primitive equations of oceanic dynamics

Speaker(s) Daniel Boutros University of Cambridge
Date 15 February 2024 – 16:00 to 17:00
Venue INI Seminar Room 1
Session Title The mathematical analysis of the primitive equations of oceanic dynamics
Event [ADI] Anti-diffusive dynamics: from sub-cellular to astrophysical scales
Abstract

In this talk I will first present a survey of known results on the mathematical analysis of the primitive equations, which model large-scale oceanic and atmospheric dynamics. Then I will present new results concerning an analogue of Onsager's conjecture for the inviscid primitive equations (which relates the regularity of weak solutions to the conservation of energy). The anisotropic nature of these equations allows us to introduce new types of weak solutions and prove a range of independent sufficient regularity criteria for energy conservation. Therefore there probably is a 'family' of Onsager conjectures for these equations. Furthermore, we employ the method of convex integration to show the global existence and nonuniqueness of weak solutions to the inviscid and viscous primitive equations. This is joint work with Simon Markfelder and Edriss S. Titi.

Presentation Files 42007_0.pdf

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