Partial Differential Equations

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source: Centre International de Rencontres Mathématiques     2015年8月7日
Partial Differential Equations

Jean-Yves Chemin: On the isotropic nature of the possible blow up for 3D Navier-Stokes 51:58
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities.
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 v0 with vorticity Ω0=∇×v0 in L3/2 (which implies that v0 belongs to the Sobolev space H1/2 ), 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 ℝ3 ; there holds
∫T∗0∥v(t)⋅e∥p1/2+2/p dt=∞.
We remark that all these quantities are scaling invariant under the scaling transformation of Navier-Stokes system.
Recording during the thematic meeting: "Vorticity, rotation and symmetry (III) - approaching limiting cases of fluid flows", the May 6, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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[deleted video]
Fabrice Planchon: The wave equation on a model convex domain revisited​ 51:45

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