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SUMMARY:From the d'Alembert paradox to the 1984 Kato criteria via the 1941
  1/3 Kolmogorov law and the 1949 Onsager conjecture. - Claude Bardos\, Lab
 oratoire Jacques Louis Lions
DTSTART:20191121T150000Z
DTEND:20191121T160000Z
UID:TALK125992@talks.cam.ac.uk
CONTACT:Edriss S. Titi
DESCRIPTION:My recent contributions\, with Marie Farge\, Edriss Titi\, Emi
 le Wiedemann\, Piotr and Agneska Gwiadza\, were motivated by the following
  issues:\nThe role of boundary effect in mathematical theory of fluids me
 chanic and the similarity\, in presence of these effects\, of the weak co
 nvergence in the zero viscosity limit and the statistical theory of turbul
 ence.\n\nAs a consequence. I will recall the Onsager conjecture and compar
 e it to the issue of anomalous energy dissipation. Then I will give a proo
 f of the local conservation of energy under convenient hypothesis in a dom
 ain with boundary and give supplementary condition that imply the global c
 onservation of energy in a domain with boundary and the absence of anomalo
 us energy dissipation in the zero viscosity limit of solutions of the Navi
 er-Stokes equation in the presence of no slip boundary condition. Eventual
 ly the above results are compared with several forms of a basic theorem of
  Kato in the presence of a Lipschitz solution of the Euler equations and o
 ne may insist on the fact that in such case the the absence of anomalous e
 nergy dissipation is equivalent to the persistence of regularity in the ze
 ro viscosity limit. Eventually this remark contributes\nto the resolution 
 of the d'Alembert Paradox.
LOCATION:MR 14
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