[Dottorcomp] Seminari di Matematica Applicata, 03/07/2024, Riccardo Montalto e Adrian Nachman

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Mercoledì 3 luglio 2024, alle ore 15.00 precise, presso l'aula Beltrami del
dipartimento di Matematica,

Riccardo Montalto (Università di Milano)
terrà un seminario dal titolo:

Nonlinear quasi-periodic oscillations in Fluid Mechanics,

e alle ore 16 precise,

Adrian Nachman (University of Toronto)

terrà un seminario dal titolo:
A Nonlinear Plancherel Theorem with Applications to Global Well-posedness
for a Davey-Stewartson Equation and to the Calderon Inverse Boundary Value
Problem

Abstract (Montalto)
In this talk I shall discuss some recent results about the construction of
quasi-periodic waves in Euler equations and other hydro-dynamical models in
dimension greater or equal than two. I shall discuss quasi-peridic
solutions and vanishing viscosity limit for forced Euler and Navier-Stokes
equations and the problem of constructing quasi-periodic traveling waves
bifurcating from Couette flow (and connections with inviscid damping). Time
permitting, I also discuss some results concerning the construction of
large amplitude quasi-periodic waves in MHD system and rotating fluids. The
techniques are of several kinds: Nash-Moser iterations, micro-local
analysis, analysis of resonances in higher dimension, normal form
constructions and spectral theory.

Abstract (Nachman)
 We consider a well-studied nonlinear Fourier transform in two dimensions
for which a proof of the Plancherel theorem had been a challenging open
problem.
The talk will explain the background and the main ideas involved in the
solution of this problem, as well as in the solution of two other open
problems that motivated it: global well-posedness for the defocusing DSII
equation in the mass critical case, and global uniqueness for the inverse
boundary value problem of Calderon for a class of unbounded conductivities.
Included will be two theorems of independent interest: new estimates for
classical fractional integrals, and a new result on boundedness of
pseudodifferential operators with non-smooth symbols.
All of this is joint work with Idan Regev and Daniel Tataru.

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Pagina web dei Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/
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