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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Near Resonance Approximation of Rotating Navier-St
okes Equations - Bin Cheng (University of Surrey)
DTSTART;TZID=Europe/London:20220830T160000
DTEND;TZID=Europe/London:20220830T162000
UID:TALK177656AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/177656
DESCRIPTION:We formalise the concept of near resonance for the
rotating Navier-Stokes equations\, based on which
we propose a novel way to approximate the origina
l PDE. The spatial domain is a three-dimensional f
lat torus of arbitrary aspect ratios. We prove tha
t the family of proposed PDEs are globally well-po
sed for any rotation rate and initial datum of any
size. Such approximations retain much more 3-mode
interactions\, thus more accurate\, than the conv
entional exact resonance approach. Our approach is
free from any limiting argument that requires phy
sical parameters to tend to zero or infinity\, and
is free from any small divisor argument (so estim
ates depend smoothly on the torus' aspect ratios).
The key estimate hinges on counting of integer so
lutions of Diophantine inequalities rather than Di
ophantine equations. The main results and ingredie
nts of the proofs can form part of the mathematica
l foundation of a non-asymptotic approach to nonli
near oscillatory dynamics in real-world applicatio
ns. \;\nThis is joint work with Zisis N. Sakel
laris (University of Surrey).
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