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SUMMARY:Wild Weak Solutions to Equations arising in Hydrodynamics (6/6)
DTSTART;VALUE=DATE-TIME:20200319T090000Z
DTEND;VALUE=DATE-TIME:20200319T110000Z
DTSTAMP;VALUE=DATE-TIME:20200218T100352Z
UID:indico-event-5405@indico.math.cnrs.fr
DESCRIPTION:In this course\, we will discuss the use of convex integration
to construct wild weak solutions in the context of the Euler and Navier-S
tokes equations. In particular\, we will outline the resolution of Onsager
's conjecture as well as the recent proof of non-uniqueness of weak soluti
ons to the Navier-Stokes equations.\n\nOnsager's conjecture states that we
ak solutions to the Euler equation belonging to Hölder spaces with Hölde
r exponent greater than 1/3 conserve energy\, and conversely\, there exit
weak solutionslying in any Hölder space with exponent less than 1/3 which
dissipate energy. The conjecture itself is linked to the anomalous disspo
ation of energy in turbulent flows\, which has been called the zeroth law
of turbulence.\n\nFor initial datum of finite kinetic energy\, Leray has p
roven that there exists at least one global in time finite energy weak sol
ution of the 3D Navier-Stokes equations. We prove that weak solutions of t
he 3D Navier-Stokes equations are not unique\, within a class of weak solu
tions with finite kinetic energy. The non-uniqueness of Leray-Hopf solutio
ns is the subset of a famous conjecture of Ladyzenskaja in '69\, and to da
te\, this conjecture remains open.\n\nhttps://indico.math.cnrs.fr/event/54
05/
LOCATION:IHES Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/5405/
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