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SUMMARY:Michele Coti Zelati (Imperial College London)
DTSTART:20200414T200000Z
DTEND:20200414T210000Z
DTSTAMP:20260404T094426Z
UID:mitpde/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/mitpd
 e/1/">Inviscid damping and enhanced dissipation in 2d fluids</a>\nby Miche
 le Coti Zelati (Imperial College London) as part of MIT PDE/analysis semin
 ar spring 2020\n\nLecture held in 2-135.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mitpde/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loredana Lanzani (Syracuse)
DTSTART:20200428T200000Z
DTEND:20200428T210000Z
DTSTAMP:20260404T094426Z
UID:mitpde/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/mitpd
 e/2/">On the symmetrization of Cauchy-like kernels</a>\nby Loredana Lanzan
 i (Syracuse) as part of MIT PDE/analysis seminar spring 2020\n\nLecture he
 ld in 2-135.\n\nAbstract\nIn this talk I will present new symmetrization i
 dentities for a family of Cauchy-like kernels in complex dimension one.\n\
 nSymmetrization identities of this kind were first employed in geometric m
 easure theory by\nP. Mattila\, M. Melnikov\, X. Tolsa\, J. Verdera et al.\
 , to obtain 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 pa
 rtial resolution of a long-standing open problem known as Vitushkins conje
 cture.\n\nHere we extend this analysis to a class of integration kernels t
 hat are more closely related\nto the holomorphic reproducing kernels that 
 arise in complex function theory.\nThis is joint work with Malabika Praman
 ik (U. British Columbia).\n
LOCATION:https://stable.researchseminars.org/talk/mitpde/2/
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BEGIN:VEVENT
SUMMARY:Vedran Sohinger (University of Warwick)
DTSTART:20200505T200000Z
DTEND:20200505T210000Z
DTSTAMP:20260404T094426Z
UID:mitpde/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/mitpd
 e/3/">Gibbs measures of nonlinear Schrödinger equations as limits of many
 -body quantum states</a>\nby Vedran Sohinger (University of Warwick) as pa
 rt of MIT PDE/analysis seminar spring 2020\n\nLecture held in 2-135.\n\nAb
 stract\nGibbs measures of nonlinear Schr¨odinger equations are a fundamen
 tal object used to\\nstudy low-regularity solutions with random initial da
 ta. In the dispersive PDE community\,\\nthis point of view was pioneered b
 y Bourgain in the 1990s. We study the problem of the\\nderivation of Gibbs
  measures as mean-field limits of Gibbs states in many-body quantum\\nmech
 anics.\\nWe present two approaches to this problem. The first one is based
  on a perturbative\\nexpansion in the interaction. This expansion is then 
 analysed by means of Borel resummation techniques and a graphical represen
 tation. The second approach is based on a\\nfunctional integral representa
 tion. The latter can be interpreted as a rigorous version of\\nan infinite
 -dimensional stationary phase argument. This is joint work with J¨urg Fr
 ¨ohlich\,\\nAntti Knowles\, and Benjamin Schlein.\n
LOCATION:https://stable.researchseminars.org/talk/mitpde/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Rodnianski (Princeton)
DTSTART:20200512T200000Z
DTEND:20200512T210000Z
DTSTAMP:20260404T094426Z
UID:mitpde/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/mitpd
 e/4/">Compressible fluids and singularity formation in supercritical defoc
 using Schrödinger equations</a>\nby Igor Rodnianski (Princeton) as part o
 f MIT PDE/analysis seminar spring 2020\n\nLecture held in 2-135.\n\nAbstra
 ct\nWe will discuss recent work with F. Merle\, P. Raphael and J. Szeftel\
 , where we studied\nthe problem of global regularity for a defocusing supe
 rcritical Schrodinger equation. The\ncorresponding problem had been settle
 d in the affirmative in a long series of works in\nthe sub-critical and en
 ergy critical cases and was conjectured by J. Bourgain to have a\nsimilar 
 positive answer in the supercritical case. We construct a set of smooth\, 
 nicely\ndecaying initial data for which the corresponding solutions blow u
 p in finite time with a\nhighly oscillatory behavior near singularity. The
  construction proceeds by establishing a\nlink between the Schr¨odinger a
 nd the the compressible Euler equations. It also leads to\nnew singularity
  results for the compressible Euler and Navier–Stokes equations.\n
LOCATION:https://stable.researchseminars.org/talk/mitpde/4/
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