5 papers · 1 filter
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…
Blow-up in finite or infinite time of the 2D cubic Zakharov-Kuznetsov equation
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko +1
We prove that near-threshold negative energy solutions to the 2D cubic (-critical) focusing Zakharov-Kuznetsov (ZK) equation blow-up in finite or infinite time. The proof cons…
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 +Îu +V(x)|u|^{\frac{4-2b}{N}}u = 0, \end{align} whe…