English
Endpoint maximal regularity in BMO and its application to fluid mechanics
Multi angle
Auteurs : Ogawa,Takayoshi (Auteur de la Conférence)
CIRM (Editeur )
35K45 - Initial value problems for pararabolic systems
35K55 - Nonlinear parabolic equations
35Q35 - PDEs in connection with fluid mechanics
35Q60 - PDEs in connection with optics and electromagnetic theory
42B37 - Harmonic analysis and PDE
CIRM (Editeur )
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Résumé :
We consider maximal regularity for the heat equation based on the endpoint function class BMO (the class of bounded mean oscillation). It is well known that BM O(Rn) is the endpoint class for solving the initial value problem for the incompressible Navier-Stokes equations and it is well suitable for solving such a problem ([3]) rather than the end-point homogeneous Besov spaces (cf. [1], [5]). First we recall basic properties of the function space BM O and show maximal regularity for the initial value problem of the Stokes equations ([4]). As an application, we consider the local well-posedness issue for the MHD equations with the Hall effect (cf. [2]). This talk is based on a joint work with Senjo Shimizu (Kyoto University).
Keywords : MHD system; Navier-Stokes equations; maximal regularity; BMO
Codes MSC : Keywords : MHD system; Navier-Stokes equations; maximal regularity; BMO
35K45 - Initial value problems for pararabolic systems
35K55 - Nonlinear parabolic equations
35Q35 - PDEs in connection with fluid mechanics
35Q60 - PDEs in connection with optics and electromagnetic theory
42B37 - Harmonic analysis and PDE
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 29/11/2024 Date de captation : 14/11/2024 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : PDE Format : MP4 (.mp4) - HD Durée : 01:01:14 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-11-14_Ogawa.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Mathematics of fluids in motion: Recent results and trends / Fluides en mouvement : résultats récents et perspectivesOrganisateurs de la rencontre : Danchin, Raphaël ; Necasova, Sarka Dates : 11/11/2024 - 15/11/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3108.html
Données de citation
DOI : 10.24350/CIRM.V.20270503Citer cette vidéo: Ogawa,Takayoshi (2024). Endpoint maximal regularity in BMO and its application to fluid mechanics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20270503 URI : http://dx.doi.org/10.24350/CIRM.V.20270503 |
Voir aussi
- [Multi angle] Stability threshold of 2-D Couette flow for the Navier-Stokes equations / Auteur de la Conférence Zhang, Zhifei.
- [Multi angle] The Role of Dissipation in the Existence of Time-Periodic Solutions to PDE Systems / Auteur de la Conférence Muha, Boris.
- [Multi angle] The long way of a viscous vortex dipole / Auteur de la Conférence Gallay, Thierry.
- [Multi angle] A one-dimensional model for suspension flows / Auteur de la Conférence Perrin, Charlotte.
Bibliographie
- BOURGAIN, Jean et PAVLOVIĆ, Nataša. Ill-posedness of the Navier–Stokes equations in a critical space in 3D. Journal of Functional Analysis, 2008, vol. 255, no 9, p. 2233-2247. - https://doi.org/10.1016/j.jfa.2008.07.008
- KAWASHIMA, Shuichi, NAKASATO, Ryosuke, et OGAWA, Takayoshi. Global well-posedness and time-decay of solutions for the compressible Hall-magnetohydrodynamic system in the critical Besov framework. Journal of Differential Equations, 2022, vol. 328, p. 1-64. - https://doi.org/10.1016/j.jde.2022.03.017
- KOCH, Herbert et TATARU, Daniel. Well-posedness for the Navier–Stokes equations. Advances in Mathematics, 2001, vol. 157, no 1, p. 22-35. - https://doi.org/10.1006/aima.2000.1937
- OGAWA, Takayoshi et SHIMIZU, Senjo. Maximal regularity for the Cauchy problem of the heat equation in BMO. Mathematische Nachrichten, 2022, vol. 295, no 7, p. 1406-1442. - https://doi-org/10.1002/mana.201900506
- WANG, Baoxiang. Ill-posedness for the Navier–Stokes equations in critical Besov spaces B˙∞, q− 1. Advances in Mathematics, 2015, vol. 268, p. 350-372. - https://doi.org/10.1016/j.aim.2014.09.024
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