Strichartz estimates for geophysical fluid equations using Fourier restriction theory
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 f...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.618/ |
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| author | Gentil, Corentin Tabary, Côme |
| author_facet | Gentil, Corentin Tabary, Côme |
| author_sort | Gentil, Corentin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0d6220c4c9304f98addcb47ec74a6980 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-0d6220c4c9304f98addcb47ec74a69802025-02-07T11:23:31ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G101155118110.5802/crmath.61810.5802/crmath.618Strichartz estimates for geophysical fluid equations using Fourier restriction theoryGentil, Corentin0Tabary, Côme1Département de Mathématiques et Applications, ENS-PSL, 45 rue d’Ulm 75005 Paris, FranceDépartement de Mathématiques et Applications, ENS-PSL, 45 rue d’Ulm 75005 Paris, FranceWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.618/Geophysical fluidsFourier restriction theoremsStrichartz estimates |
| spellingShingle | Gentil, Corentin Tabary, Côme Strichartz estimates for geophysical fluid equations using Fourier restriction theory Comptes Rendus. Mathématique Geophysical fluids Fourier restriction theorems Strichartz estimates |
| title | Strichartz estimates for geophysical fluid equations using Fourier restriction theory |
| title_full | Strichartz estimates for geophysical fluid equations using Fourier restriction theory |
| title_fullStr | Strichartz estimates for geophysical fluid equations using Fourier restriction theory |
| title_full_unstemmed | Strichartz estimates for geophysical fluid equations using Fourier restriction theory |
| title_short | Strichartz estimates for geophysical fluid equations using Fourier restriction theory |
| title_sort | strichartz estimates for geophysical fluid equations using fourier restriction theory |
| topic | Geophysical fluids Fourier restriction theorems Strichartz estimates |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.618/ |
| work_keys_str_mv | AT gentilcorentin strichartzestimatesforgeophysicalfluidequationsusingfourierrestrictiontheory AT tabarycome strichartzestimatesforgeophysicalfluidequationsusingfourierrestrictiontheory |