## View abstract

### 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. document.getElementById('cloakf89dd5c18140176a9c5d19c0c0a5577f').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyf89dd5c18140176a9c5d19c0c0a5577f = 'lgf&#97;r&#97;h' + '&#64;'; addyf89dd5c18140176a9c5d19c0c0a5577f = addyf89dd5c18140176a9c5d19c0c0a5577f + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_textf89dd5c18140176a9c5d19c0c0a5577f = 'lgf&#97;r&#97;h' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloakf89dd5c18140176a9c5d19c0c0a5577f').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyf89dd5c18140176a9c5d19c0c0a5577f + '\'>'+addy_textf89dd5c18140176a9c5d19c0c0a5577f+'<\/a>';

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).