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SUMMARY:General Solution Theory for the Stochastic Navier-Stokes Equations
DTSTART:20240208T151500
DTEND:20240208T161500
DTSTAMP:20260508T082119Z
UID:c1d60bb5342f4c1fc365f1dbbcc38c65af5b54cbfaad09d2f7fc29a7
CATEGORIES:Conferences - Seminars
DESCRIPTION:Daniel Goodair\nAbstract: The Navier-Stokes Equations are the
  fundamental models for viscous fluid dynamics\, but no prediction is perf
 ect. Introducing randomness into differential equations has long been the 
 answer to uncertainty quantification\, inviting new methodologies for thes
 e stochastic perturbations to best refine our predictions. Recent developm
 ents in the modelling literature point to the significance oftransport noi
 se\, where the stochastic integral depends on the gradient of the solution
 \; analytically\, this unbounded noise breaks classical frameworks built f
 or the study of nonlinear SPDEs.\n\nIn this talk\, I shall present general
  well-posedness results for SPDEs with applications to the Navier-Stokes E
 quations under Stochastic Advection by Lie Transport. We consider three 
 different solution types of increasing strength\, applied for martingale w
 eak\, weak and strong solutions. Particular attention is given to the case
  of a physical boundary\, where existence results for transport noise were
  previously unknown. I shall briefly comment on some inviscid limit result
 s for the equations\, and the prospect of a regularisation by noise phenom
 enon. \n 
LOCATION:Tukey room   MA B1 504
STATUS:CONFIRMED
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