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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On Energy Conservation for the hydrostatic Euler e
 quations: an Onsager Conjecture - Daniel Boutros (
 University of Cambridge)
DTSTART;TZID=Europe/London:20220615T110000
DTEND;TZID=Europe/London:20220615T120000
UID:TALK175613AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175613
DESCRIPTION:Onsager's conjecture states that the incompressibl
 e Euler equations conserve kinetic energy (the L^2
  norm in space) if the velocity field is H&ouml\;l
 der continuous in space with exponent bigger than 
 1/3. In case the exponent is less than 1/3 energy 
 dissipation can occur. We consider an analogue of 
 Onsager's conjecture for the hydrostatic Euler equ
 ations. These equations arise from the Euler equat
 ions under the assumption of the hydrostatic balan
 ce\, as well as the small aspect ratio limit (in w
 hich the vertical scale is much smaller compared t
 o the horizontal scales). Unlike the Euler equatio
 ns\, in the case of the hydrostatic Euler equation
 s the vertical velocity is one degree spatially le
 ss regular compared to the horizontal velocities. 
 The fact that the equations are anisotropic in reg
 ularity and nonlocal makes it possible to prove a 
 range of sufficient criteria for energy conservati
 on\, which are independent of each other. This mea
 ns that there probably is a 'family' of Onsager co
 njectures for these equations. This is joint work 
 with Simon Markfelder and Edriss S. Titi.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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