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SUMMARY:Singular flows\, zeroth order pseudodifferential operators and spe
 ctra - Nilima Nigam (Simon Fraser)
DTSTART:20240606T140000Z
DTEND:20240606T150000Z
UID:TALK217135@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:The propagation of internal gravity waves in stratified media 
 (such as those found in ocean basins and lakes) leads to the development o
 f attractors. These structures accumulate much of the wave energy and can 
 make the fluid flow highly singular. These questions have been the subject
  of fascinating recent analytical developments by de Verdiere & Saint-Raym
 ond\, and Zworski and co-workers\, who examine a simplified model which re
 tains many of the important features. These are related to a certain zerot
 h-order pseudodifferential operator.\n\n In this talk\, we first review th
 e physical phenomenon\, and the (highly simplified) model evolution proble
 m. We next describe a high-accuracy computational method to solve the evol
 ution problem\, whose long-term behaviour is known to be non-square-integr
 able. Then\, we use similar tools to discretize the corresponding eigenval
 ue problem. Since the eigenvalues are embedded in a continuous spectrum\, 
 their computation is based on viscous approximations. We also study the lo
 ng-term evolution of the dynamics of the system. This is joint work with J
 avier Almonacid.\n
LOCATION:Centre for Mathematical Sciences\, MR12
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