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SUMMARY:Sanchit Chaturvedi (Stanford University)
DTSTART;VALUE=DATE-TIME:20201103T171500Z
DTEND;VALUE=DATE-TIME:20201103T182500Z
DTSTAMP;VALUE=DATE-TIME:20230208T061830Z
UID:PDEseminarUPenn/1
DESCRIPTION:Title: Vector field method for collisional kinetic models\nby Sanchit
Chaturvedi (Stanford University) as part of Partial Differential Equation
s Seminar at UPenn\n\n\nAbstract\nThe vector field method developed by Kla
inerman has been widely successful in the study of wave equations and gene
ral relativity. Recently\, the vector field approach has been adapted to u
nderstand the dispersion due to the transport operator in both collisionle
ss and collisional kinetic models. As an application of the approach\, I w
ill briefly discuss the stability of vacuum for Landau equation results (d
ue to Luk for the moderately soft potentials case and due to me for the ha
rd potentials case). Next\, I will discuss my recent result on stability o
f vacuum for Boltzmann equation with moderately soft potentials. \nIn addi
tion to understanding dispersion\, the vector field approach can be used t
o understand phase mixing in the weakly collisional regime. To illustrate
that I will present a work in progress (in collaboration with Jonathan Luk
and Toan Nguyen) where we consider the Vlasov--Poisson--Landau equation i
n the weakly collisional regime and prove that the for appropriately small
sized data\, the solution exhibits enhanced dissipation and Landau dampin
g.\n
LOCATION:https://researchseminars.org/talk/PDEseminarUPenn/1/
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SUMMARY:Quoc hung Nguyen (Shanghaitech university)
DTSTART;VALUE=DATE-TIME:20210406T161500Z
DTEND;VALUE=DATE-TIME:20210406T171500Z
DTSTAMP;VALUE=DATE-TIME:20230208T061830Z
UID:PDEseminarUPenn/2
DESCRIPTION:Title: Well-posedness of the Muskat problem\nby Quoc hung Nguyen (Sha
nghaitech university) as part of Partial Differential Equations Seminar at
UPenn\n\n\nAbstract\nI will present local and global well-posedness of th
e 2d muskat problem with viscosity jump and surface tension when the inter
face is a graph.\n\nZoom link will be posted at the following web page at
least two hours before the talk: www.math.upenn.edu/events/seminars/partia
l-differential-equations-seminar\n\nJoin Zoom Meeting\nhttps://upenn.zoom.
us/j/98243656806?pwd=dlFHOHZ0bW1SWjJUMStqUENBeUxCZz09\n\nMeeting ID: 982 4
365 6806\nPasscode: 641370\n
LOCATION:https://researchseminars.org/talk/PDEseminarUPenn/2/
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