Logo

Mathematical Sciences Research Institute

Home » Graduate Student Working Group: Ocean boundary layer formation: the quasi-geostrophic model & TBA

Seminar

Graduate Student Working Group: Ocean boundary layer formation: the quasi-geostrophic model & TBA May 19, 2021 (11:10 AM PDT - 12:10 PM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Mostafa Hassan (Johns Hopkins University), Gabriela Lopez-Ruiz (Sorbonne University)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Video

Low Regularity Almost-Global Well-Posedness for Quasilinear Wave Equations

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

1st Speaker: Gabriela López Ruiz (Sorbonne Université)

Title: Ocean boundary layer formation: the quasi-geostrophic model

Abstract: We will talk about the impact of small-scale irregularities on the coasts on oceanic circulation at the mesoscale. We study a singular perturbation problem from meteorology known as the quasi-geostrophic model. A complete asymptotic analysis is performed assuming rough coasts do not present a particular structure. In particular, we establish the well-posedness of the boundary layer system and the asymptotic behavior of the solution far from the boundary. We investigate the action of pseudodifferential operators in nonlocalized Sobolev spaces and use ergodic properties to deal with the singular behavior of the eastern boundary layer profiles. These results generalize the ones of Bresch and Gérard-Varet (Commun. Math. Phys. 253, 81–119 (2005)) for periodic roughness.



2nd Speaker : Mostafa Hassan (University of Wisconsin Madison)

Title: TBA

Abstract: The goal of our work is to prove global well-posedness for quasilinear wave equations with as few  assumptions on the initial data as possible. Current partial results, including almost-global well-posedness and  globalwell-posedness with sub-optimal but reduced regularity assumptions will be presented, as well as the general idea we believe can yield a more optimal result. The proofs utilize the ghost weight method, localization  in time and space adapted to the light cone geometry, and careful Sobolev-type embeddings that require as few vector fields as possible.

No Notes/Supplements Uploaded

Low Regularity Almost-Global Well-Posedness for Quasilinear Wave Equations