91 citations · 311 across the 34 of their papers we have counts for
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Threshold solutions for the cubic INLS: the energy-critical case
Luccas Campos, Luiz Gustavo Farah, Jason Murphy
We study the energy-critical cubic inhomogeneous NLS equation . In this work, we prove the existence of special solutions with…
Threshold solutions for the cubic INLS: the energy-subcritical case
Luccas Campos, Luiz Gustavo Farah, Jason Murphy
We revisit the work [L. Campos and J. Murphy, SIAM J. Math. Anal., 55 (2023), pp. 3807--3843], which classified the dynamics of solutions at the ground state threshold for cu…
The focusing energy-critical nonlinear Schrödinger system with power-type growth nonlinearities in the radial case
Luiz Gustavo Farah, Maicon Hespanha
This work is concerned with a coupled system of focusing nonlinear Schrödinger equations involving general power-type nonlinearities in the energy-critical setting for dimensions $…
Minimal mass blow-up solutions for a inhomogeneous NLS equation
Mykael Cardoso, Luiz Gustavo Farah
We consider the inhomogeneous nonlinear Schrödinger (INLS) equation in \begin{align}\label{inls} i \partial_t u +Δu +V(x)|u|^{\frac{4-2b}{N}}u = 0, \end{align} where…
A note on the well-posedness in the energy space for the generalized ZK equation posed on
Luiz Gustavo Farah, Luc Molinet
In this note, we prove the local well-posedness in the energy space of the -generalized Zakharov-Kuznetsov equation posed on $ \R\times \T $ for any power non-linearity $ k\ge 2…
Blow-up for the 3D intercritical inhomogeneous NLS with inverse-square potential
Luccas Campos, Mykael Cardoso, Luiz Gustavo Farah
In this paper we study the focusing inhomogeneous 3D nonlinear Schrödinger equation with inverse-square potential in the mass-supercritical and energy-subcritical regime. We first…