Year: 2024
Type: article
Abstract: We prove Strichartz estimates for the semigroups associated to stratified and/or rotating inviscid geophysical fluids using Fourier restriction theory. We prove new results for rotating stratified fluids, and recover results from Koh, Lee, Takada, 2014 for rotation only, and from Lee, Takada, 2017 for stratification only. Our restriction estimates are obtained by the slicing method (Nicola 2009), which relies on the well-known Tomas–Stein theorem for 2-dimensional spheres. To our knowledge, such a method has never been used in this setting. Moreover, when the fluid is stratified, our approach yields sharp estimates, showing that the slicing method captures all the available curvature of the surfaces of interest.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.618
Authors: Corentin Gentil, Côme Tabary
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404061936