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Norman Noguera

Publications and source records attributed to Norman Noguera.

6 recordsLinked to original sources
arXiv2024

Blow-up solutions to a class of nonlinear coupled Schrödinger systems with power-type-growth nonlinearities

In this work we consider a system of nonlinear Schrödinger equations whose nonlinearities satisfy a power-type-growth. First, we prove that the Cauchy problem is local and global well-posedness in $L^2$ and $H^1$. Next, we establish the existence of ground state solutions. Then we use these solutions to study the dichotomy of global existence versus blow-up in finite time. Similar results were presented in the reference Noguera N. and Pastor A. 2022 https://doi.org/10.1142/S0219199720500236 for the special case when the growth of the nonlinearities was quadratic. Here we will extend them to systems with nolinearities of order $p$ (cubic, quartic and so on). Finally, we recover some known results for two particular systems, one with quadratic and the other with cubic growth nolinearities.

math.AP↗
arXiv2021

Scattering for quadratic-type Schrödinger systems in dimension five without mass-resonance

In this paper we study the scattering of non-radial solutions in the energy space to coupled system of nonlinear Schrödinger equations with quadratic-type growth interactions in dimension five without the mass-resonance condition. Our approach is based on the recent technique introduced by Dodson and Murphy, which relies on an interaction Morawetz estimate. It is proved that any solution below the ground states scatters in time.

math.AP↗
arXiv2020

Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six

In this work, we show the existence of ground state solutions for an $l$-component system of non-linear Schrödinger equations with quadratic-type growth interactions in the energy-critical case. They are obtained analyzing a critical Sobolev-type inequality and using the concentration-compactness method. As an application, we prove the existence of blow-up solutions of the system without the mass-resonance condition in dimension six (and five), when the initial data is radial.

math.AP↗
arXiv2019

On a system of Schrödinger equations with general quadratic-type nonlinearities

In this work we study a system of Schrödinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in terms on the ground state solutions associated with the corresponding elliptic system, which in turn are obtained by applying variational methods. By using the concentration-compactness method we also investigate the nonlinear stability/instability of the ground states.

math.AP↗
arXiv2018

On the dynamics of a quadratic Schrödinger system in dimension $n=5$

In this work we give a sharp criterion for the global well-posedness, in the energy space, for a system of nonlinear Schrödinger equations with quadratic interaction in dimension $n=5$. The criterion is given in terms of the charge and energy of the ground states associated with the system, which are obtained by minimizing a Weinstein-type functional. The main result is then obtained in view of a sharp Gagliardo-Nirenberg-type inequality.

math.AP↗