10 citations · 19 across the 23 of their papers we have counts for
31 papers
Global well-posedness for the modified dispersion-generalized Benjamin-Ono equations
Mikaela Baldasso, Simão Correia, Thyago S. R. Santos
In this short note, we prove the global well-posedness of the modified dispersion-generalized Benjamin-Ono equation with dispersion , $$\partial_t u + D^α\partial_x u + u^2\…
Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations
Simão Correia, Gonçalo Pereira, Thyago S. R. Santos
Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction…
Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation
Simão Correia, Shinya Kinoshita
We consider the Cauchy problem associated with the modified Zakharov-Kuznetsov equation over . Taking into consideration the associated dispersive effects, we introdu…
Nonlinear smoothing implies improved lower bounds on the radius of spatial analyticity for nonlinear dispersive equations
Mikaela Baldasso, Simão Correia
We provide a roadmap to establish improved lower bounds on the decay rate of the uniform radius of analyticity for a given nonlinear dispersive equation, reducing the proble…
Improved global well-posedness for the quartic Korteweg-de Vries equation
Simão Correia
We prove that the quartic Korteweg-de Vries equation is globally well-posed for real-valued initial data in , .
Classification and stability of positive solutions to the NLS equation on the -metric graph
Francisco Agostinho, Simão Correia, Hugo Tavares
Given and , we present a complete classification of the positive -solutions of the equation on the -metric graph (consisting of tw…
Sharp local well-posedness and nonlinear smoothing for dispersive equations through frequency-restricted estimates
Simão Correia, Filipe Oliveira, Jorge Drumond Silva
We consider the problem of establishing nonlinear smoothing as a general feature of nonlinear dispersive equations, i.e. the improved regularity of the integral term in Duhamel's f…
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^…
A note on bifurcations from eigenvalues of the Dirichlet-Laplacian with arbitrary multiplicity
Simão Correia, Mário Figueira
In this short note, we consider the elliptic problem on a smooth domain , $N\ge 1…
Perturbation at blow-up time of self-similar solutions for the modified Korteweg-de Vries equation
Simão Correia, Raphaël Côte
We prove a first stability result of self-similar blow-up for the modified KdV equation on the line. More precisely, given a self-similar solution and a sufficiently small regular…
On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
Vanessa Barros, Simão Correia, Filipe Oliveira
We study the nonlinear Schrödinger equation with initial data in , where and $2<p<2…
Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces
Simão Correia
We consider the Benjamin-Ono equation on the real line for initial data in weighted Sobolev spaces. After the application of the gauge transform, the flow is shown to be Lipschitz…
Mass-transfer instability of ground-states for Hamiltonian Schrödinger systems
Simão Correia, Filipe Oliveira, Jorge D. Silva
We study generic semilinear Schrödinger systems which may be written in Hamiltonian form. In the presence of a single gauge invariance, the components of a solution may exchange ma…
Nonlinear smoothing for dispersive PDE: a unified approach
Simão Correia, Jorge Drumond Silva
In several cases of nonlinear dispersive PDEs, the difference between the nonlinear and linear evolutions with the same initial data, i.e. the integral term in Duhamel's formula, e…
A generalized Complex Ginzburg-Landau Equation: global existence and stability results
Simão Correia, Mário Figueira
We consider the complex Ginzburg-Landau equation with two pure-power nonlinearities and a damping term. After proving a general global existence result, we focus on the existence a…
Self-similar dynamics for the modified Korteweg-de Vries equation
Simão Correia, Raphaël Côte, Luis Vega
We prove a local well posedness result for the modified Korteweg-de Vries equation in a critical space designed so that is contains self-similar solutions. As a consequence, we can…
Some stability results for the complex Ginzburg-Landau equation
Simão Correia, Mário Figueira
Using some classical methods of dynamical systems, stability results and asymptotic decay of strong solutions for the complex Ginzburg-Landau equation (CGL), $$ \partial_t u = (a +…
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
Simão Correia, Raphaël Côte, Luis Vega
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted W^{1,\infty} aroun…
Scattering theory for the Schrödinger-Debye System
Simão Correia, Filipe Oliveira
We study the Schrödinger-Debye system over iu_t+\frac 12Δu=uv,\quad μv_t+v=λ|u|^2 and establish the global existence and scattering of small solutions for initial da…
Finite speed of disturbance for the nonlinear Schrödinger equation
Simão Correia
We consider the Cauchy problem for the nonlinear Schrödinger equation on the whole space. After introducing a weaker concept of finite speed of propagation, we show that the concat…
Local Cauchy theory for the nonlinear Schrödinger equation in spaces of infinite mass
Simão Correia
We consider the Cauchy problem for the nonlinear Schrödinger equation on , where the initial data is in . We prove loca…
On a nonlinear Schrödinger system arising in quadratic media
Adán Corcho, Simão Correia, Filipe Oliveira +1
We consider the quadratic Schrödinger system where , in…
Existence and stability of spatial plane waves for the incompressible Navier-Stokes in
Simão Correia, Mário Figueira
We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a family of global spatial plane wave solu…
Spatial plane waves for the nonlinear Schrödinger equation: local existence and stability results
Simão Correia, Mário Figueira
We consider the Cauchy problem for the nonlinear Schrödinger equation on , , , . We introduce new functiona…