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Endpoint maximal regularity in BMO and its application to fluid mechanics
Multi angle
Authors : Ogawa,Takayoshi (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/11/2024 Conference Date : 14/11/2024 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : PDE Format : MP4 (.mp4) - HD Video Time : 01:01:14 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-11-14_Ogawa.mp4 
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Information on the Event
Event Title : Mathematics of fluids in motion: Recent results and trends / Fluides en mouvement : résultats récents et perspectivesEvent Organizers : Danchin, Raphaël ; Necasova, Sarka Dates : 11/11/2024 - 15/11/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3108.html
Citation Data
DOI : 10.24350/CIRM.V.20270503Cite this video as: 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 |
See Also
- [Multi angle] Stability threshold of 2-D Couette flow for the Navier-Stokes equations / Author of the conference Zhang, Zhifei.
- [Multi angle] The Role of Dissipation in the Existence of Time-Periodic Solutions to PDE Systems / Author of the conference Muha, Boris.
- [Multi angle] The long way of a viscous vortex dipole / Author of the conference Gallay, Thierry.
- [Multi angle] A one-dimensional model for suspension flows / Author of the conference Perrin, Charlotte.
Bibliography
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- 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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