Luiz Gustavo Farah Dias

Universidade Federal de Minas Gerais, Brazil

Title: On the mass-critical inhomogeneous NLS equation

Abstract: We consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation 

\[

i u_t +\Delta u+|x|^{-b}|u|^{\frac{4-2b}{N}} u = 0,        x \in \mathbb{R}^N,

\]

with $N\geq 1$ and $0<b< 1$, which is a generalization of the classical nonlinear Schr\"odinger equation (NLS). Since the scaling invariant Sobolev index is zero, the equation is called mass-critical. 

In this talk we discuss some blow-up results in the non-radial setting, obtained in collaboration with Mykael Cardoso (UFPI-Brazil).

This work is partially supported by CNPq, CAPES and FAPEMIG-Brazil.