59 citations · 78 across the 20 of their papers we have counts for
20 papers · 1 filter
Existence and equicontinuity of solutions to the Kirchhoff--Pohozaev wave equation
Luccas Campos, Rowan Killip, Monica Visan
It was recently discovered by Boiti--Manfrin that a variant of the Kirchhoff wave equation introduced by Pohozaev admits infinitely many conserved quantities. In this paper, we obt…
Scattering and nonlinear recovery for the 1 NLW with localized nonlinearity
Luccas Campos, Jason Murphy, Renzo Scarpelli
We consider the wave equation in 1 with a spatially-localized cubic nonlinearity. We establish scattering in a weighted space and demonstrate the injectivity of the scattering m…
Threshold dynamics for the radial cubic NLS with repulsive inverse-square potential
Luke Baker, Luccas Campos, Jason Murphy +1
We classify the dynamics of radial solutions at the (radial) ground state threshold for the cubic NLS in the presence of a repulsive inverse-square potential.
Determination of radial nonlocal nonlinearities from the scattering map
Luccas Campos, Rowan Killip, Jason Murphy +1
We show that the small-data scattering map uniquely determines the nonlinearity for a class of nonlinear Schrödinger equations with radial, Hartree-type nonlinearities. Our assumpt…
Large data scattering for the defocusing -dispersion generalized Benjamin-Ono equation in the energy space
Luccas Campos, Felipe Linares, Thyago S. R. Santos
We study the defocusing -dispersion generalized Benjamin-Ono equation. For every even integer , we prove that solutions with initial data in the energy space $H^{\fracα…
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…
Sharp well-posedness for the -dispersion generalized Benjamin-Ono equations: Short and long time results
Luccas Campos, Felipe Linares, Thyago S. R. Santos
We consider the -dispersion generalized Benjamin-Ono (-DGBO) equations. For nonlinearities with power , we establish local and global well-posedness results for the…
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…
Threshold solutions for cubic Schrödinger systems
Luccas Campos, Ademir Pastor
We consider the following Scrödinger system $$\begin{cases}\displaystyle i\partial_t u + Δu +(|u|^2+β|v|^2) u= 0, \\ \displaystyle i\partial_t v + Δv +(|v|^2+β|u|^2) v = 0,\end{cas…
Sharp well-posedness and ill-posedness results for the inhomogeneous NLS equation
Luccas Campos, Simão Correia, Luiz Gustavo Farah
We consider the initial value problem associated to the inhomogeneous nonlinear Schrö\-din\-ger equation, \begin{equation} iu_t + Δu +μ|x|^{-b}|u|^αu=0, \quad u_0\in H^s(\mathbb R^…
Averaging for the dispersion-managed NLS
Luccas Campos, Jason Murphy, Tim Van Hoose
We establish global-in-time averaging for the -critical dispersion-managed nonlinear Schrödinger equation in the fast dispersion management regime. In particular, in the case…
Threshold solutions for the intercritical inhomogeneous NLS
Luccas Campos, Jason Murphy
We consider the focusing inhomogeneous nonlinear Schrödinger equation in , \begin{equation} i\partial_t u + Δu + |x|^{-b}|u|^{2}u=0,{equation} where $0 < b <\tfr…
Scattering for the non-radial inhomogenous biharmonic NLS equation
Luccas Campos, Carlos M. Guzmán
We consider the focusing inhomogeneous biharmonic nonlinear Schrödinger equation in , \begin{equation} iu_t + Δ^2 u - |x|^{-b}|u|^αu=0 \end{equation} when $b > 0…
A Virial-Morawetz approach to scattering for the non-radial inhomogeneous NLS
Luccas Campos, Mykael Cardoso
Consider the focusing inhomogeneous nonlinear Schrödinger equation in , when and in the intercritical ca…
On the inhomogeneous NLS with inverse-square potential
Luccas Campos, Carlos M. Guzmán
We consider the inhomogeneous nonlinear Schrödinger equation with inverse-square potential in $$ i u_t + \mathcal{L}_a u+λ|x|^{-b}|u|^αu = 0,\;\;\mathcal{L}_a=Δ-\fra…
Threshold solutions for the nonlinear Schrödinger equation
Luccas Campos, Luiz Gustavo Farah, Svetlana Roudenko
We study the focusing NLS equation in in the mass-supercritical and energy-subcritical (or intercritical) regime, with data at the mass-energy threshold $ \mat…
Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrödinger equation
Luccas Campos, Mykael Cardoso
We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in , , with finite-variance initial d…
Scattering of radial solutions to the Inhomogeneous Nonlinear Schrödinger Equation
Luccas Campos
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}…
On the critical norm concentration for the inhomogeneous nonlinear Schrödinger equation
Luccas Campos, Mykael Cardoso
We consider the inhomogeneous nonlinear Schrödiger equation (INLS) in and show the -norm concentration for the…