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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Calvin Khor\, Beijing Normal University\n\nAbstract: In the pur
suit of understanding vortex filaments for the 3D Euler equation (solutions
with concentrated vorticity)\, we describe sharp fronts and almost sharp f
ronts for the SQG equation\, which are analogues of vortex filaments that c
an be discussed in a rigourous setting. We further discuss a singular gener
alisation of the SQG model for which given an almost-sharp front\, a specia
l `spine’ curve can be chosen in a measure theoretic way that formally surv
ives in the limit. In the second part of the talk\, we discuss a different
system\, called the Navier—Stokes—Boussinesq system\, for which we cannot w
rite the explicit evolution equation for the contour dynamics of the sharp
front. Nevertheless\, the regularity of a sharp front can be shown to be pr
eserved globally in time. We show that this can be extended to the setting
with fractional dissipation\, until right before the equation with critical
dissipation\, which does not seem to have a well-posedness theory for temp
erature patch solutions.
DTEND:20210220T020000Z
DTSTAMP:20240913T173423Z
DTSTART:20210220T010000Z
LOCATION:
SEQUENCE:0
SUMMARY:Analysis and PDE Seminar: Sharp fronts for models of incompressible
fluids
UID:tag:localist.com\,2008:EventInstance_35917385782268
URL:https://calendar.usc.edu/event/analysis_and_pde_seminar_426
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