English
On the Navier-Stokes equations on surfaces
Multi angle
Auteurs : Simonett, Gieri (Auteur de la Conférence)
CIRM (Editeur )
35B40 - Asymptotic behavior of solutions of PDE
35Q30 - Stokes and Navier-Stokes equations
35Q35 - PDEs in connection with fluid mechanics
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2576/Slides/simonett.pdf
CIRM (Editeur )
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Résumé :
I will consider the motion of an incompressible viscous fluid on compact surfaces without boundary. Local in time well-posedness is established in the framework of $L_{p}$-$L_{q}$ maximal regularity for initial values in critical spaces. It will be shown that the set of equilibria consists exactly of the Killing vector fields. Each equilibrium is stable and any solution starting close to an equilibrium converges at an exponential rate to a (possibly different) equilibrium. In case the surface is two-dimensional, it will be shown that any solution with divergence free initial value in $L_{2}$ exists globally and converges to an equilibrium.
Keywords : surface Navier-Stokes equations; surface Stokes operator; critical spaces; Killing vector fields; Korn's inequality; global existence
Codes MSC : Keywords : surface Navier-Stokes equations; surface Stokes operator; critical spaces; Killing vector fields; Korn's inequality; global existence
35B40 - Asymptotic behavior of solutions of PDE
35Q30 - Stokes and Navier-Stokes equations
35Q35 - PDEs in connection with fluid mechanics
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2576/Slides/simonett.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 13/06/2022 Date de captation : 09/05/2022 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : Analysis and its Applications Format : MP4 (.mp4) - HD Durée : 00:41:52 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-05-09_Simonett.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2022 - Conference: Nonlinear PDEs in Fluid Dynamics / Chaire Jean-Morlet 2022 - Conférence : EDP non-linéaires en dynamique des fluidesOrganisateurs de la rencontre : Danchin, Raphaël ; Hieber, Matthias ; Monniaux, Sylvie ; Perrin, Charlotte Dates : 09/05/2022 - 13/05/2022 Année de la rencontre : 2022 URL Congrès : https://www.chairejeanmorlet.com/2576.html
Données de citation
DOI : 10.24350/CIRM.V.19917103Citer cette vidéo: Simonett, Gieri (2022). On the Navier-Stokes equations on surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19917103 URI : http://dx.doi.org/10.24350/CIRM.V.19917103 |
Voir aussi
- [Multi angle] Global solutions for one dimensional dispersive models / Auteur de la Conférence Tataru, Daniel.
- [Multi angle] Energy balance for 2D incompressible fluid flow / Auteur de la Conférence Nussenzveig Lopes, Helena.
- [Virtualconference] On the inviscid limit for the Navier-Stokes equations / Auteur de la Conférence Kukavica, Igor.
- [Multi angle] Large global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions / Auteur de la Conférence Brandolese, Lorenzo.
Bibliographie
- SIMONETT, Gieri et WILKE, Mathias. $ H^\infty $-calculus for the surface Stokes operator and applications. arXiv preprint arXiv:2111.12586, 2021. - https://arxiv.org/abs/2111.12586
- PRÜSS, Jan, SIMONETT, Gieri, et WILKE, Mathias. On the Navier–Stokes equations on surfaces. Journal of Evolution Equations, 2021, vol. 21, no 3, p. 3153-3179. - http://dx.doi.org/10.1007/s00028-020-00648-0
- PRÜSS, Jan, SIMONETT, Gieri, et WILKE, Mathias. Critical spaces for quasilinear parabolic evolution equations and applications. Journal of Differential Equations, 2018, vol. 264, no 3, p. 2028-2074. - https://doi.org/10.1016/j.jde.2017.10.010
- PRÜSS, Jan et SIMONETT, Gieri. Moving interfaces and quasilinear parabolic evolution equations. Basel : Birkhäuser, 2016. - http://dx.doi.org/10.1007/978-3-319-27698-4
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