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SUMMARY:Onsager-type conjectures for boundary-driven and geophysical flows
  [Oberseminar Analysis]
DTSTART:20251120T131500Z
DTEND:20251120T141500Z
DTSTAMP:20260308T042100Z
UID:indico-event-934@math-events.uni-bonn.de
CONTACT:zemas@iam.uni-bonn.de
DESCRIPTION:Speakers: Daniel Boutros (Cambridge University)\n\nOnsager's c
 onjecture states that 1/3 is the critical spatial (Hölder) regularity thr
 eshold for energy conservation by weak solutions of the incompressible Eul
 er equations. We consider Onsager’s conjecture for the Euler equations i
 n the case of a bounded domain\, as boundary effects play a crucial role i
 n hydrodynamic turbulence. We present a regularity result for the pressure
  in the Euler equations\, which is fundamental for the proof of the conser
 vation part of the Onsager conjecture (in the presence of boundaries). As 
 an essential part of the proof\, we introduce a new weaker notion of bound
 ary condition which we show to be necessary by means of an explicit exampl
 e. Moreover\, we derive this new boundary condition rigorously from the we
 ak formulation of the Euler equations.\n \nIn addition\, we consider an a
 nalogue of Onsager’s conjecture for the hydrostatic Euler equations (als
 o known as the inviscid primitive equations of oceanic and atmospheric dyn
 amics). The anisotropic nature of these equations allows us to introduce n
 ew types of weak solutions and prove a range of independent sufficient cri
 teria for energy conservation. Therefore there probably is a ‘family’ 
 of Onsager conjectures for these equations. Furthermore\, we employ the me
 thod of convex integration to show the nonuniqueness of weak solutions to 
 the inviscid and viscous primitive equations (and also the Prandtl equatio
 ns)\, and to construct examples of solutions that do not conserve energy i
 n the inviscid case. If time allows\, I will also present some recent resu
 lts on a model from sea-ice dynamics\, which is the elastic-viscous-plasti
 c sea-ice model. These are joint works with Claude Bardos\, Xin Liu\, Simo
 n Markfelder\, Marita Thomas and Edriss S. Titi.\n\nhttps://math-events.un
 i-bonn.de/event/934/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/934/
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