L. Farah

activity

20082026

most citedLocal solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation

91 citations · 311 across the 34 of their papers we have counts for

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Showing 2016 · math.APShow all

5 papers · 2 filters

math.AP2016★ 1 cited

On the lack of compactness and existence of maximizers for some Airy-Strichartz inequalities

Luiz Gustavo Farah, Henrique Versieux

This work is devoted to prove a linear profile decomposition for the Airy equation in $H ˙_{x}^{s_{k}} (R)$ , where $s_{k} = (k - 4) /2 k$ and $k > 4$ . We also apply this decompositio…

math.AP2016★ 5 cited

Nonlinear Profile Decomposition and the Concentration Phenomenon for Supercritical Generalized KdV Equations

Luiz Gustavo Farah, Brian Pigott

A nonlinear profile decomposition is established for solutions of supercritical generalized Korteweg-de Vries equations. As a consequence, we obtain a concentration result for fini…

math.AP2016

Global well-posedness and blow-up on the energy space for the Inhomogeneous Nonlinear Schrödinger Equation

Luiz Gustavo Farah

We consider the supercritical inhomogeneous nonlinear Schrödinger equation (INLS) $i \partial_{t} u + Δ u + ∣ x ∣^{- b} ∣ u ∣^{2 σ} u = 0,$ where $(2 - b) / N < σ < (2 - b) / (N - 2)$ and $0 < b < min {2, N}$ . We…

math.AP2016

Scattering for the radial 3D cubic focusing inhomogeneous nonlinear Schrödinger equation

Luiz Farah, Carlos Guzmán

The purpose of this work is to study the 3D focusing inhomogeneous nonlinear Schrödinger equation $i u_{t} + Δ u + ∣ x ∣^{- b} ∣ u ∣^{2} u = 0,$ where $0 < b < 1/2$ . Let $Q$ be the ground state…

math.AP2016

Scattering for a 3D coupled nonlinear Schrödinger system

Luiz Gustavo Farah, Ademir Pastor

We consider the three-dimensional cubic nonlinear Schrödinger system \begin{equation*} \begin{cases} i\partial_tu+Δu+(|u|^2+β|v|^2)u=0,\\ i\partial_tv+Δv+(|v|^2+β|u|^2)v=0. \end{ca…