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SUMMARY:Michele Coti Zelati (Imperial College London)
DTSTART;VALUE=DATE-TIME:20200414T200000Z
DTEND;VALUE=DATE-TIME:20200414T210000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075335Z
UID:mitpde/1
DESCRIPTION:Title: I
nviscid damping and enhanced dissipation in 2d fluids\nby Michele Coti
Zelati (Imperial College London) as part of MIT PDE/analysis seminar spri
ng 2020\n\nLecture held in 2-135.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/mitpde/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loredana Lanzani (Syracuse)
DTSTART;VALUE=DATE-TIME:20200428T200000Z
DTEND;VALUE=DATE-TIME:20200428T210000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075335Z
UID:mitpde/2
DESCRIPTION:Title: O
n the symmetrization of Cauchy-like kernels\nby Loredana Lanzani (Syra
cuse) as part of MIT PDE/analysis seminar spring 2020\n\nLecture held in 2
-135.\n\nAbstract\nIn this talk I will present new symmetrization identiti
es for a family of Cauchy-like kernels in complex dimension one.\n\nSymmet
rization identities of this kind were first employed in geometric measure
theory by\nP. Mattila\, M. Melnikov\, X. Tolsa\, J. Verdera et al.\, to ob
tain a new proof of $L^2(\\mu)$ regularity of the Cauchy transform (with
µ a positive Radon measure in C)\, which ultimately led to the a partial
resolution of a long-standing open problem known as Vitushkins conjecture.
\n\nHere we extend this analysis to a class of integration kernels that ar
e more closely related\nto the holomorphic reproducing kernels that arise
in complex function theory.\nThis is joint work with Malabika Pramanik (U.
British Columbia).\n
LOCATION:https://researchseminars.org/talk/mitpde/2/
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BEGIN:VEVENT
SUMMARY:Vedran Sohinger (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200505T200000Z
DTEND;VALUE=DATE-TIME:20200505T210000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075335Z
UID:mitpde/3
DESCRIPTION:Title: G
ibbs measures of nonlinear Schrödinger equations as limits of many-body q
uantum states\nby Vedran Sohinger (University of Warwick) as part of M
IT PDE/analysis seminar spring 2020\n\nLecture held in 2-135.\n\nAbstract\
nGibbs measures of nonlinear Schr¨odinger equations are a fundamental obj
ect used to\\nstudy low-regularity solutions with random initial data. In
the dispersive PDE community\,\\nthis point of view was pioneered by Bourg
ain in the 1990s. We study the problem of the\\nderivation of Gibbs measur
es as mean-field limits of Gibbs states in many-body quantum\\nmechanics.\
\nWe present two approaches to this problem. The first one is based on a p
erturbative\\nexpansion in the interaction. This expansion is then analyse
d by means of Borel resummation techniques and a graphical representation.
The second approach is based on a\\nfunctional integral representation. T
he latter can be interpreted as a rigorous version of\\nan infinite-dimens
ional stationary phase argument. This is joint work with J¨urg Fr¨ohlich
\,\\nAntti Knowles\, and Benjamin Schlein.\n
LOCATION:https://researchseminars.org/talk/mitpde/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Rodnianski (Princeton)
DTSTART;VALUE=DATE-TIME:20200512T200000Z
DTEND;VALUE=DATE-TIME:20200512T210000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075335Z
UID:mitpde/4
DESCRIPTION:Title: C
ompressible fluids and singularity formation in supercritical defocusing S
chrödinger equations\nby Igor Rodnianski (Princeton) as part of MIT P
DE/analysis seminar spring 2020\n\nLecture held in 2-135.\n\nAbstract\nWe
will discuss recent work with F. Merle\, P. Raphael and J. Szeftel\, where
we studied\nthe problem of global regularity for a defocusing supercritic
al Schrodinger equation. The\ncorresponding problem had been settled in th
e affirmative in a long series of works in\nthe sub-critical and energy cr
itical cases and was conjectured by J. Bourgain to have a\nsimilar positiv
e answer in the supercritical case. We construct a set of smooth\, nicely\
ndecaying initial data for which the corresponding solutions blow up in fi
nite time with a\nhighly oscillatory behavior near singularity. The constr
uction proceeds by establishing a\nlink between the Schr¨odinger and the
the compressible Euler equations. It also leads to\nnew singularity result
s for the compressible Euler and Navier–Stokes equations.\n
LOCATION:https://researchseminars.org/talk/mitpde/4/
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