Mykael Cardoso - UFPI/UFMG

Título:

On the phenomenon of critical norm concentration for INLS.

Resumo:

The Inhomogeneous Nonlinear Schrödinger equation (INLS) have been attracting attention from both physical and mathematical point of view in recent years.

In this talk we discuss about the $L^2$-norm concentration for the finite time blow-up solutions to INLS in the $L^2$-critical case. We also present an alternative proof for the classification of minimal mass blow-up solutions to INLS, first proved by Genoud and Combet [2]. The main tool is Profile decomposition (see Hmidi and Keraani [3]).

This is a joint work with Luccas Campos (Florida International University - FIU).

References:

[1] L. Campos and M. Cardoso , On the critical norm concentration for the inhomogeneous nonlinear Schrödinger equation., arXiv preprint arXiv:1810.09086, 2018.

[2] V. Combet and F. Genoud, Classification minimal mass blow-up solutions for an $L^2$ critical inhomogeneous NLS, Journal of Evolution Equations, 16(2): 483-500, 2016.

[3] T. Hmidi and S. Keraani, Blow up theory for the critical nonlinear Schrödinger equations revisited, International Mathematics Research Notices, 2005(2): 2815-2828.