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On the Navier-Stokes equations on surfaces
Multi angle
Authors : Simonett, Gieri (Author of the conference)
CIRM (Publisher )
35B40 - Asymptotic behavior of solutions of PDE
35Q30 - Stokes and Navier-Stokes equations
35Q35 - PDEs in connection with fluid mechanics
Additional resources :
https://www.cirm-math.fr/RepOrga/2576/Slides/simonett.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/2576/Slides/simonett.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/06/2022 Conference Date : 09/05/2022 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:41:52 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-05-09_Simonett.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2022 - Conference: Nonlinear PDEs in Fluid Dynamics / Chaire Jean-Morlet 2022 - Conférence : EDP non-linéaires en dynamique des fluidesEvent Organizers : Danchin, Raphaël ; Hieber, Matthias ; Monniaux, Sylvie ; Perrin, Charlotte Dates : 09/05/2022 - 13/05/2022 Event Year : 2022 Event URL : https://www.chairejeanmorlet.com/2576.html
Citation Data
DOI : 10.24350/CIRM.V.19917103Cite this video as: 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 |
See Also
- [Multi angle] Global solutions for one dimensional dispersive models / Author of the conference Tataru, Daniel.
- [Multi angle] Energy balance for 2D incompressible fluid flow / Author of the conference Nussenzveig Lopes, Helena.
- [Virtualconference] On the inviscid limit for the Navier-Stokes equations / Author of the conference Kukavica, Igor.
- [Multi angle] Large global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions / Author of the conference Brandolese, Lorenzo.
Bibliography
- 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
Imagette Video
