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SUMMARY:Near Resonance Approximation of Rotating Navier-Stokes Equations -
  Bin Cheng (University of Surrey)
DTSTART:20220830T150000Z
DTEND:20220830T152000Z
UID:TALK177656@talks.cam.ac.uk
DESCRIPTION:We formalise the concept of near resonance for the rotating Na
 vier-Stokes equations\, based on which we propose a novel way to approxima
 te the original PDE. The spatial domain is a three-dimensional flat torus 
 of arbitrary aspect ratios. We prove that the family of proposed PDEs are 
 globally well-posed for any rotation rate and initial datum of any size. S
 uch approximations retain much more 3-mode interactions\, thus more accura
 te\, than the conventional exact resonance approach. Our approach is free 
 from any limiting argument that requires physical parameters to tend to ze
 ro or infinity\, and is free from any small divisor argument (so estimates
  depend smoothly on the torus' aspect ratios). The key estimate hinges on 
 counting of integer solutions of Diophantine inequalities rather than Diop
 hantine equations. The main results and ingredients of the proofs can form
  part of the mathematical foundation of a non-asymptotic approach to nonli
 near oscillatory dynamics in real-world applications.&nbsp\;\nThis is join
 t work with Zisis N. Sakellaris (University of Surrey).
LOCATION:No Room Required
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