Mathematical analysis of atmospheric models with moisture

Abstract:

In this talk I will present some recent results concerning the global regularity of the three-dimensional Primitive Equations of oceanic and atmospheric dynamics with various anisotropic viscosity and turbulence mixing diffusion. However, in the non-viscous (inviscid) case it can be shown that there is a one-parameter family of initial data for which the corresponding smooth solutions of the inviscid Primitive Equations develop finite-time singularities (blowup).

Capitalizing on the above results, one is able to provide rigorous justification for the derivation of the Primitive Equations of planetary scale oceanic dynamics from the three-dimensional Navier-Stokes equations, for vanishing small values of the aspect ratio of the depth to horizontal width.

In addition, we will also show the global well-posedeness of the coupled three-dimensional viscous Primitive Equations with a micro-physics phase change moisture model for cloud formation.

Furthermore, we will also consider the singular limit behavior of a tropical atmospheric model with moisture, as $ε → 0$, where $ε >0$ is a moisture phase transition small convective adjustment relaxation time parameter.

With the mass cancellation of in-person conferences and seminars due to the coronavirus pandemic, research communities need novel ways to stay connected. Inspired by the One World Probability Seminar, the One World PDE Seminar aims to provide such a venue for the PDE community, accessible to as many researchers as possible.

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This talk is hosted by University of BATH. Link to the talk site.