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Session S22 - Deterministic and probabilistic aspects of nonlinear evolution equations

Thursday, July 22, 18:55 ~ 19:25 UTC-3

Blow-up solutions of the intercritical inhomogeneous NLS equation

Luiz Gustavo Farah

Universidade Federal de Minas Gerais, Brasil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation \[ i u_t +\Delta u+|x|^{-b}|u|^{2\sigma} u = 0, \,\,\, x\in \mathbb{R}^N, \] with $N\geq 3$ and $b\in (0,2)$. We focus on the intercritical case, where the scaling invariant Sobolev index $s_c=\frac{N}{2}-\frac{2-b}{2\sigma}$ satisfies $s_c\in (0,1)$. In this talk, for initial data in $\dot H^{s_c}\cap \dot H^1$, we discuss the existence of blow-up solutions and also a lower bound for the blow-up rate in the radial and non-radial settings.

Joint work with Mykael Cardoso (Universidade Federal do Piauí, Brasil).

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