Nonlinear Dispersive PDE & Harmonic Analysis · IMECC–UNICAMP

Publications

Publications

Selected research outputs. Where available, journal pages, DOIs, or arXiv links are provided.

Published Articles

  • A. J. Mendez. On the propagation of regularity for solutions of the dispersion generalized Benjamin–Ono equation. Analysis & PDE 13(8) (2020), 2399–2440.
  • A. J. Mendez. On some properties in solutions of the fractional KdV equation. Journal of Differential Equations 269(11) (2020), 9051–9089.
  • F. Linares; G. Ponce; A. J. Mendez. Asymptotic behavior of solutions of the dispersion generalized Benjamin–Ono equation. Journal of Dynamical and Differential Equations 33(2) (2021), 971–984.
  • C. Muñoz; F. Poblete; J. Pozo; A. J. Mendez. On local energy decay for large solutions of the Zakharov–Kuznetsov equation. Communications in Partial Differential Equations 46(8) (2021).
  • F. Linares; A. J. Mendez. On long time behavior of solutions of the Schrödinger–Korteweg–de Vries system. SIAM Journal on Mathematical Analysis 53(4) (2021).
  • R. Freire; O. Riaño; A. J. Mendez. On some regularity properties for the dispersive generalized Benjamin–Ono–Zakharov–Kuznetsov equation. Journal of Differential Equations 322 (2022), 135–179.
  • A. J. Mendez. On Kato’s smoothing effect for a fractional version of the Zakharov–Kuznetsov equation. Discrete & Continuous Dynamical Systems 43(5) (2023), 2047–2101.
  • A. J. Mendez. On the propagation of regularity for solutions of the Zakharov–Kuznetsov equation. Analysis and Applications (2023).
  • C. Muñoz; F. Poblete; J. Pozo; A. J. Mendez. Long time asymptotics of large data in the Kadomtsev–Petviashvili models. Nonlinearity 37(5) (2024).
  • F. Linares; D. Pilod; A. J. Mendez. Well-posedness for the extended Schrödinger–Benjamin–Ono system. Vietnam Journal of Mathematics 52(4) (2024).
  • O. Riaño; A. J. Mendez. On decay properties for solutions of the Zakharov–Kuznetsov equation. Nonlinear Analysis: Real World Applications 81 (2025).

Preprints

  • A. J. Mendez; O. Riaño. A monotonicity formula for the fractional Laplacian and instability results for the Shrira equation. Preprint, arXiv:2509.14870, 2025.

Work in Progress

  • With Marcelo Nogueira: Analytic solutions of the Schrödinger–Korteweg–de Vries system under minimal conditions of regularity.
  • With Felipe Linares: On the Schrödinger–Benjamin–Ono system: global well-posedness, the existence of solitary waves, and asymptotic behavior.
  • With Oscar Riaño: Instability of the solutions of the Shrira equation in dimension 2.
  • Analytic smoothing effect solutions of the dispersive generalized Benjamin–Ono equation in spaces with low regularity.