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
Masahiro Yamamoto: Inverse problems for fluid dynamics 44:43
Bruno Després: Mathematical properties of hierarchies of reduced MHD models 1:03:05
François Delarue: Mean-field analysis of an excitatory neuronal network: application to [...]
Francis Filbet: On hybrid method for rariefied gas dynamics: Boltzmann vs. Navier-Stokes models 59:49
Michael Weinstein: Waves and microstructures 1:01:49
Faouzi Triki: Inverse scattering problems with multi-frequency data 35:03
Guillaume Bal: High-contrast high-resolution coupled physics imaging modalities 50:51
Lionel Roques: Uniqueness of coefficients by strong maximum principle 50:06
David Dos Santos Ferreira: The anisotropic Calderon problem 49:08
Leif Arkeryd: On low temperature kinetic theory; spin diffusion, anyons, Bose Einstein condensates 35:00
Julien Barré: From Vlasov-Poisson-Fokker-Planck to incompressible Euler equations 39:01
Chiara Saffirio: From the Hartree-Fock dynamics to the Vlasov equation 35:19
Delphine Salort: Around a Fokker-Planck equation modeling neuronal networks 50:51
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Nicola Visciglia: Scattering for NLS in ℝd×𝕋 49:27
Mourad Bellassoued: Stable determination of coefficients in the dynamical Schrödinger [...] 56:54
Lauri Oksanen: On the boundary control method 58:11
Samuli Siltanen: Reconstruction methods for ill-posed inverse problems - Part 1 53:01
Samuli Siltanen: Reconstruction methods for ill-posed inverse problems - Part 2 49:47
Pierre Raphaël: Singularity formation in semi linear dispersing / parabolic problem 1:00:35
Juan Luis Vázquez: The theory of nonlinear diffusion with fractional operators 1:00:50
Patrick Gérard: Resonant two-soliton interaction for the one dimensional half wave equation 1:01:37
Panagiota Daskalopoulos: Ancient solutions to geometric flows 1:01:21
Richard Melrose: The wave equation for Weil-Petersson metrics 1:05:29
Jeffrey Galkowski: Quantum Sabine law for resonances in transmission problems 50:12
Christopher Judge: Hyperbolic triangles with no positive Neumann eigenvalues 58:01
Julie Rowlett: A Polyakov formula for sectors 47:08
Joaquin Fontbona: Non-local Lokta-Volterra cross diffusion systems - part 1 1:29:39
Joaquin Fontbona: Non-local Lokta-Volterra cross diffusion systems - part 2 1:31:10
Laurent Desvillettes: Spatially structured population dynamics: the point of view of PDEs - part 1 1:30:33
Laurent Desvillettes : Spatially structured population dynamics: the point of view of PDEs - part 2 1:31:55
László Székelyhidi: The H-Principle and Turbulence 46:03
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Colin Guillarmou: Correspondence between Ruelle resonances and quantum resonances ... 57:15
Peter Hintz: The stability of Kerr-de Sitter black holes 57:55
Anke Pohl: Isomorphisms between eigenspaces of slow and fast transfer operators 58:06
Gabriel Rivière: Correlation spectrum of Morse-Smale flows 57:47
David Borthwick: Asymptotics of resonances for hyperbolic surfaces 1:00:29
Andras Vasy: Microlocal analysis for Kerr-de Sitter black holes 1:01:18
Andrea Pulita: An overview on some recent results about p-adic differential equations ... 52:24
Andrea D'Agnolo : On the Riemann-Hilbert correspondence for irregular holonomic D-modules 1:25:18
Martin Hairer: Weak universality of the KPZ equation with arbitrary nonlinearities 54:31
Ping Zhang: Large time behavior os solutions to 3-D MHD system with initial data near equilibrium 49:52
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Evelyne Miot: An asymptotic regime for the Vlasov-Poisson system 28:16
Josef Málek: On the analysis of a class of thermodynamically compatible viscoelastic... 1:03:16
Camillo De Lellis: The Onsager Theorem 1:02:58
Giovanni Peccati: Cancellations in random nodal sets 43:04
Interview at Cirm: Martin Hairer 19:36
Bernard Helffer: Spectral theory and semi-classical analysis for the complex Schrödinger operator 42:05
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Catherine Sulem: Soliton Resolution for Derivative NLS equation 56:55
Michael Weinstein: Dispersive waves in novel 2d media; Honeycomb structures, Edge States ... 54:43
Evgenii Kuznetsov: ​​Solitons vs collapses 53:34
Valeria Banica: Dynamics of almost parallel vortex filaments 45:18
Yvon Martel: Interactions of solitary waves for the nonlinear Schrödinger equations 36:37
[deleted video]
Fabrice Planchon: The wave equation on a model convex domain revisited​ 51:45