arXiv subjects

Luccas Campos

Publications and source records attributed to Luccas Campos.

20 records · Page 2Linked to original sources

arXiv2020

Scattering of radial solutions to the Inhomogeneous Nonlinear Schrödinger Equation

We prove scattering below the mass-energy threshold for the focusing inhomogeneous nonlinear Schrödinger equation \begin{equation} iu_t + Δu + |x|^{-b}|u|^{p-1}u=0, \end{equation} when $b \geq 0$ and $N > 2$ in the intercritical case $0 < s_c <1$. This work generalizes the results of Farah and Guzmán [9], allowing a broader range of values for the parameters $p$ and $b$. We use a modified version of Dodson-Murphy's approach [6], allowing us to deal with the inhomogeneity. The proof is also valid for the classical nonlinear Schrödinger equation ($b = 0$), extending the work in [6] for radial solutions in all intercritical cases.

math.AP↗

arXiv2018

On the critical norm concentration for the inhomogeneous nonlinear Schrödinger equation

We consider the inhomogeneous nonlinear Schrödiger equation (INLS) in $\mathbb{R}^N$ $$i \partial u_t + Δu + |x|^{-b} |u|^{2σ}u = 0,$$ and show the $L^2$-norm concentration for the finite time blow-up solutions in the $L^2$-critical case, $σ=\frac{2-b}{N}$. Moreover, we provide an alternative for the classification of minimal mass blow-up solutions first proved by Genoud and Combet [4]. For the case $\frac{2-b}{N} < σ< \frac{2-b}{N-2}$, we show results regarding the $L^p$-critical norm concentration, generalizing the argument of Holmer and Roudenko [16] to the INLS setting.

math.AP↗