Publications

Preprints

[29] S. Correia, R. Côte, Sharp blow-up stability for self-similar solutions of the modified Korteweg-de Vries equation (2024), arXiv:2402.16423

[28] L. Campos, S. Correia, L. G. Farah, Sharp well-posedness and ill-posedness results for the inhomogeneous NLS equation (2022), arXiv:2210.07060 

Publications

[27] S. Correia, F. Oliveira, J. D. Silva, Sharp local well-posedness and nonlinear smoothing for dispersive equations through frequency-restricted estimates, to appear in SIAM J. Math. Anal. (2024), arXiv:2302.03575

[26] S. Correia, Improved global well-posedness for the quartic Korteweg-de Vries equation, to appear in Proc. AMS (2024), arxiv:2310.13497

[25] S. Correia, R. Côte, Perturbation at blow-up time of self-similar solutions for the modified Korteweg-de Vries equation, ARMA (2024) 248, 25.

[24] F. Agostinho, S. Correia, H. Tavares, Classification and stability of positive solutions to the NLS equation on the T-metric graph, Nonlinearity (2023) 37, no. 2.

[23] S. Correia, M. Figueira, A note on bifurcations from eigenvalues of the Dirichlet-Laplacian with arbitrary multiplicity, Nonlinear Differ. Equ. Appl. (2023) 30, 37.

[22] S. Correia, F. Oliveira, J. D. Silva, Mass-transfer instability of ground-states for Hamiltonian Schrödinger systems, J. Anal. Math.  (2022), 148, 681–710. 

[21] V. Barros, S. Correia, F. Oliveira, On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity, Differential Integral Equations (2022), 35(7/8): 371-392 

[20] S. Correia, M. Figueira, A generalized Complex Ginzburg-Landau Equation: global existence and stability results, Comm. Pure Appl. Anal. (2021), vol. 20(5) 2021-2038. 

[19] S. Correia, Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces, Nonlinear Analysis (2021), vol. 205, 112227.

[18] S. Correia, R. Côte, L. Vega, Self-Similar Dynamics for the Modified Korteweg–de Vries Equation, International Mathematics Research Notices, (2020), rnz383.

[17] S. Correia, J. D. Silva, Nonlinear smoothing for dispersive PDE: A unified approach. J. Differential Equations 269 (2020), no. 5, 4253–4285. 

[16] S. Correia, R. Côte, L. Vega, Asymptotics in Fourier space of self-similar solutions to the modified Korteweg–de Vries equation. J. Math. Pures Appl. (9) 137 (2020), 101–142. 

[15] S. Correia, M. Figueira, Some stability results for the complex Ginzburg–Landau equation, Communications in Contemporary Mathematics 22 (2019), no. 08.

[14] S. Correia, Finite speed of disturbance for the nonlinear Schrödinger equation. Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), no. 6, 1405–1419. 

[13] A. Corcho, S. Correia, F. Oliveira, J. D. Silva, On a nonlinear Schrödinger system arising in quadratic media. Commun. Math. Sci. 17 (2019), no. 4, 969–987. 

[12] S. Correia, M. Figueira, Some L^∞ solutions of the hyperbolic nonlinear Schrödinger equation and their stability. Adv. Differential Equations 24 (2019), no. 1-2, 1–30. 

[11] S. Correia, F. Oliveira, Scattering theory for the Schrödinger-Debye system. Nonlinearity 31 (2018), no. 7, 3203–3227. 

[10] S. Correia, Local Cauchy theory for the nonlinear Schrödinger equation in spaces of infinite mass. Rev. Mat. Complut. 31 (2018), no. 2, 449–465. 

[9] S. Correia, M. Figueira, Existence and stability of spatial plane waves for the incompressible Navier-Stokes in R^3. J. Math. Fluid Mech. 20 (2018), no. 1, 189–197. 

[8] S. Correia, M. Figueira, Spatial plane waves for the nonlinear Schrödinger equation: local existence and stability results. Comm. Partial Differential Equations 42 (2017), no. 4, 519–555. 

[7] S. Correia, F. Oliveira, H. Tavares, Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d≥3 equations. J. Funct. Anal. 271 (2016), no. 8, 2247–2273. 

[6] S. Correia, Ground-states for systems of M coupled semilinear Schrödinger equations with attraction-repulsion effects: characterization and perturbation results. Nonlinear Anal. 140 (2016), 112–129. 

[5] S. Correia, Stability of ground-states for a system of M coupled semilinear Schrödinger equations. NoDEA Nonlinear Differential Equations Appl. 23 (2016), no. 3, Art. 26, 14 pp. 

[4] S. Correia.  Characterization of ground-states for a system of M coupled semilinear Schrödinger equations and applications. J. Differential Equations 260 (2016), no. 4, 3302–3326. 

[3] T. Cazenave, S. Correia, F. Dickstein, F. B. Weissler,  A Fujita-type blowup result and low energy scattering for a nonlinear Schrödinger equation. São Paulo J. Math. Sci. 9 (2015), no. 2, 146–161. 

[2] S. Correia, Blowup for the nonlinear Schrödinger equation with an inhomogeneous damping term in the L^2-critical case. Commun. Contemp. Math. 17 (2015), no. 3, 1450030, 16 pp. 

[1] S. Correia, L. Sanchez, Progressive waves in the Fisher-Kolmogorov model—a modern classic. (Portuguese) Bol. Soc. Port. Mat. No. 67 (2012), 165–184.