Simão Correia

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math.AP2025

Sharp local well-posedness for the SchrÃ¶dinger-Korteweg-de Vries system

SimÃ£o Correia, Felipe Linares, Jorge Drumond Silva

We prove a sharp local existence result for the SchrÃ¶dinger-Korteweg-de Vries system with initial data in $H^{k} (R) \times H^{s} (R)$ . The proof is based on the concep…

math.AP2024

Sharp local existence and nonlinear smoothing for dispersive equations with higher-order nonlinearities

SimÃ£o Correia, Pedro Leite

We consider a general nonlinear dispersive equation with monomial nonlinearity of order $k$ over $R^{d}$ . We construct a rigorous theory which states that higher-order nonli…