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CATEGORIES:Applied and Computational Analysis
SUMMARY:From the d'Alembert paradox to the 1984 Kato crite
ria via the 1941 1/3 Kolmogorov law and the 1949 O
nsager conjecture. - Claude Bardos\, Laboratoire J
acques Louis Lions
DTSTART;TZID=Europe/London:20191121T150000
DTEND;TZID=Europe/London:20191121T160000
UID:TALK125992AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/125992
DESCRIPTION:My recent contributions\, with Marie Farge\, Edris
s Titi\, Emile Wiedemann\, Piotr and Agneska Gwiad
za\, were motivated by the following issues:\nThe
role of boundary effect in mathematical theory of
fluids mechanic and the similarity\, in presence
of these effects\, of the weak convergence in the
zero viscosity limit and the statistical theory o
f turbulence.\n\nAs a consequence. I will recall t
he Onsager conjecture and compare it to the issue
of anomalous energy dissipation. Then I will give
a proof of the local conservation of energy under
convenient hypothesis in a domain with boundary an
d give supplementary condition that imply the glob
al conservation of energy in a domain with boundar
y and the absence of anomalous energy dissipation
in the zero viscosity limit of solutions of the Na
vier-Stokes equation in the presence of no slip bo
undary condition. Eventually the above results are
compared with several forms of a basic theorem of
Kato in the presence of a Lipschitz solution of t
he Euler equations and one may insist on the fact
that in such case the the absence of anomalous ene
rgy dissipation is equivalent to the persistence o
f regularity in the zero viscosity limit. Eventual
ly this remark contributes\nto the resolution of t
he d'Alembert Paradox.
LOCATION:MR 14
CONTACT:Edriss S. Titi
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