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CATEGORIES:Analysis seminar
SUMMARY:Convergence problems for singular stochastic dynam
ics. - Younes Zine\, University of Edinburgh
DTSTART:20221114T160000Z
DTEND:20221114T170000Z
UID:TALK4990AT
URL:/talk/index/4990
DESCRIPTION:Over the last twenty years there has been signific
ant progress in the well-posedness study of singul
ar stochastic PDEs in both parabolic and dispersiv
e settings. In this talk\, I will discuss some con
vergence problems for singular stochastic nonlinea
r PDEs. In a seminal work\, Da Prato and Debussche
(2003) established well-posedness of the stochast
ic quantization equation\, also known as the parab
olic Φk+12-model in the two-dimensional case. More
recently\, Gubinelli\, Koch\, Oh\, and Tolomeo pr
oved the corresponding well-posedness for the cano
nical stochastic quantization equation\, also know
n as the hyperbolic Φk+12-model in the two-dimensi
onal case. In the first part of this talk\, I will
describe convergence of the hyperbolic Φk+12-mode
l to the parabolic Φk+12-model. In the dispersive
setting\, Bourgain (1996) established well-posedne
ss for the dispersive Φ42-model (=deterministic cu
bic nonlinear Schrödinger equation) on the two-dim
ensional torus with Gibbsian initial data. In the
second part of the talk\, I will discuss the conve
rgence of the stochastic complex Ginzburg-Landau e
quation (= complex-valued version of the parabolic
Φ42-model) to the dispersive Φ42-model at statist
ical equilibrium.
LOCATION:WATN-LT B (101)
CONTACT:Yuzhao Wang
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