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On the isotropic nature of the possible blow up for 3D Navier-Stokes
Post-edited
Authors : Chemin, Jean-Yves (Author of the conference)
CIRM (Publisher )
35Q30 - Stokes and Navier-Stokes equations
CIRM (Publisher )
Abstract :
The purpose of the talk will be the proof of the following result for the homogeneous incompressible Navier-Stokes system in dimension three: given an initial data $v_0$ with vorticity $\Omega_0= \nabla \times v_0$ in $L^{\tfrac{3}{2}}$ (which implies that $v_0$ belongs to the Sobolev space $H^{\tfrac{1}{2}}$ ), we prove that the solution $v$ given by the classical Fujita-Kato theorem blows up in a finite time $T^*$ only if, for any $p$ in ]4,6[ and any unit vector $e$ in $\mathbb{R}^3$ ; there holds
$\int_{0}^{T^*}\left \| v(t)\cdot e\right \|^p_{\frac{1}{2}+\frac{2}{p}}dt=\infty $.
We remark that all these quantities are scaling invariant under the scaling transformation of Navier-Stokes system.
MSC Codes : $\int_{0}^{T^*}\left \| v(t)\cdot e\right \|^p_{\frac{1}{2}+\frac{2}{p}}dt=\infty $.
We remark that all these quantities are scaling invariant under the scaling transformation of Navier-Stokes system.
35Q30 - Stokes and Navier-Stokes equations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/06/14 Conference Date : 06/05/14 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : PDE Format : QuickTime (.mov) Video Time : 00:51:57 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-05-06_Chemin.mp4 
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Information on the Event
Event Title : Vorticity, rotation and symmetry (III) - approaching limiting cases of fluid flows / Vorticité, rotation et symétrie (III) – analyse des situations limites en théorie des fluidesEvent Organizers : Farwig, Reinhard ; Neustupa, Jiri ; Penel, Patrick Dates : 05/05/14 - 09/05/14 Event Year : 2014 Event URL : https://www.cirm-math.fr/Archives/?EX=in...
Citation Data
DOI : 10.24350/CIRM.V.18493103Cite this video as: Chemin, Jean-Yves (2014). On the isotropic nature of the possible blow up for 3D Navier-Stokes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18493103 URI : http://dx.doi.org/10.24350/CIRM.V.18493103 |
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