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SUMMARY:James Michael Leahy (Imperial)
DTSTART:20210616T134500Z
DTEND:20210616T143000Z
DTSTAMP:20260423T024719Z
UID:YRbGSA/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/YRbGSA/19/">
 The incompressible Euler system with rough path advection</a>\nby James Mi
 chael Leahy (Imperial) as part of Young Researchers between Geometry and S
 tochastic Analysis 2021\n\n\nAbstract\nThe incompressible Euler’s equati
 ons are a mathematical model of an incompressible inviscid fluid. We will 
 discuss some aspects of a perturbation of the Euler system by a rough-in-t
 ime\, divergence-free\, Lie-advecting vector field. We are inspired by the
  problem of parametrizing unmodelled phenomena and representing sources of
  uncertainty in mathematical fluid dynamics. We will begin by presenting a
  geometric fluid dynamics inspired variational principle for the equations
  and the corresponding Kelvin balance law. Then we will give sufficient co
 nditions on the data to obtain i) local well-posedness of the system in an
 y dimension in $L^2$-Sobolev spaces and ii) a Beale-Kato-Majda (BKM) blow-
 up criterion in terms of the $L_t^1L^\\infty_x$-norm of the vorticity. The
  $L^p$-norms of the vorticity are conserved in two dimensions\, which yiel
 ds global well-posedness and a Wong-Zakai approximation theorem for the st
 ochastic version of the equation in two dimensions. \n\nThis talk is based
  on joint work with Dan Crisan\, Darryl Holm and Torstein Nilssen.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/19/
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