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Sharp blow-up stability for self-similar solutions of the modified Korteweg-de Vries equation
Simão Correia, Raphaël Côte
We consider the modified Korteweg-de Vries equation. Given a self-similar solution, and a subcritical perturbation of any size, we prove that there exists a unique solution to the…
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…
Blowup for the nonlinear Schrödinger equation with an inhomogeneous damping term in the critical case
Simão Correia
We consider the nonlinear Schrödinger equation with -critical exponent and an inhomogeneous damping term. By using the tools developed by Merle and Raphael, we prove the exist…
Characterization of ground-states for a system of coupled semilinear Schrödinger equations and applications
Simão Correia
We focus on the study of ground-states for the system of coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. General results regarding existe…