Seminar
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| Location: | SLMath: Online/Virtual |
To participate in this seminar, please register here: https://www.msri.org/seminars/25657
Low Regularity Almost-Global Well-Posedness for Quasilinear Wave Equations
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.
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