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math.AP2022
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^…
math.AP2022
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…
math.AP2022
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…