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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

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.