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SUMMARY:On Energy Conservation for the hydrostatic Euler equations: an Ons
 ager Conjecture - Daniel Boutros (University of Cambridge)
DTSTART:20220615T100000Z
DTEND:20220615T110000Z
UID:TALK175613@talks.cam.ac.uk
DESCRIPTION:Onsager's conjecture states that the incompressible Euler equa
 tions conserve kinetic energy (the L^2 norm in space) if the velocity fiel
 d is H&ouml\;lder continuous in space with exponent bigger than 1/3. In ca
 se the exponent is less than 1/3 energy dissipation can occur. We consider
  an analogue of Onsager's conjecture for the hydrostatic Euler equations. 
 These equations arise from the Euler equations under the assumption of the
  hydrostatic balance\, as well as the small aspect ratio limit (in which t
 he vertical scale is much smaller compared to the horizontal scales). Unli
 ke the Euler equations\, in the case of the hydrostatic Euler equations th
 e vertical velocity is one degree spatially less regular compared to the h
 orizontal velocities. The fact that the equations are anisotropic in regul
 arity and nonlocal makes it possible to prove a range of sufficient criter
 ia for energy conservation\, which are independent of each other. This mea
 ns that there probably is a 'family' of Onsager conjectures for these equa
 tions. This is joint work with Simon Markfelder and Edriss S. Titi.
LOCATION:Seminar Room 2\, Newton Institute
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