2018 Analysis of Equations Arising from Incompressible Fluid System
Some open problems on the control of 1D partial differential equations
Prof. Jean-Michel Coron (University of Sorbonne, France)
2018.06.28 10:30-11:30, N820
Asymptotic behavior of a wave equation
Dr. Deng Yu (Courant Institute of New York University, USA)
2018.07.05, 16:20-17:20, N913
Abstract: We adapt the method of spacetime resonance of Germain-Masmoudi-Shatah to the study of wave equations, and establish the asymptotic behavior for a model equation, which is related to the "weak null condition" introduced by Lindblad-Rodnianski. This is joint work with Fabio Pusateri.
On the relation between the Talbot effect and the flow patterns associated with noncircular jets (I), (II), (III)
Prof. Luis Vega (Dpto. de Matemáticas, UPV/EHU, Spain)
Abstract: In this talk I shall present a conjecture about the need to use the Talbot effect, that firstly appeared in optics, to understand some turbulent phenomena, as the flow patterns associated to noncircular jets generated by nozzles with corners. These patterns will be modeled by the so called Localized Induction Approximation (LIA) of the evolution of vortex filaments. More concretely, I will show that LIA is a nonlinear geometric flow that is capable of developing a nonlinear Talbot effect that, besides the usual properties of randomness, multifractality, and intermittency, has also transfer of energy.