Research interests

My research mainly focuses on the analysis of evolution PDEs describing some physical models. More precisely, my actual interests are about Nonlinear Dispersive PDEs such as Schrödinger, Schrödinger-like, Wave, Klein-Gordon, Zakharov Equations with their related problems (LWP & GWP Theory, Scattering Theory, formation of singularities, Dispersive PDEs on manifolds).

Papers

Below you find my publication list. Click on the title to get access to the (updated) preprint of the paper.

Preprints

• Local well-posedness and blow-up in the energy space for the 2D NLS with point interaction,
  joint work with Vladimir Georgiev.


• Solitons, scattering and blow-up for the nonlinear Schrödinger equation with combined power-type nonlinearities on \(\mathbb R^d\times\mathbb T\),
  joint work with Yongming Luo and Zehua Zhao.


• Invariant Gibbs dynamics for two-dimensional fractional wave equations in negative Sobolev spaces,
  joint work with Oana Pocovnicu.


• Standing waves for a Schrödinger system with three waves interaction,
  joint work with Xiao Luo, Tao Yang, and Xiaolong Yang.



Published Papers

• Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach,
  joint work with Jacopo Bellazzini and Van Duong Dinh.
  SIAM Journal on Mathematical Analysis, Vol. 56, No. 3 (2024), pp. 3110-3143.


• Ground state energy threshold and blow-up for NLS with competing nonlinearities,
  joint work with Jacopo Bellazzini and Vladimir Georgiev.
  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), Vol. XXIV (2023), 955-988.


• Dynamics of solutions to the Gross-Pitaevskii equation describing dipolar Bose-Einstein condensates,
  joint work with Jacopo Bellazzini.
  Qualitative Properties of Dispersive PDEs, Springer INdAM Series 52.


• On finite time blow-up for a 3D Davey-Stewartson system,
  Proceedings of the American Mathematical Society, 150 (2022), no. 12, 5421-5432.


• Mass-Energy threshold dynamics for dipolar Quantum Gases,
  joint work with Van Duong Dinh and Hichem Hajaiej.
  Communications in Mathematical Sciences, Vol. 20 (2022), No. 1, 165-200.


• Dynamical collapse of cylindrical symmetric dipolar Bose-Einstein condensates,
  joint work with Jacopo Bellazzini.
  Calculus of Variations and Partial Differential Equations, 60, 229 (2021).


• Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ³ nonlinear response,
  joint work with Alex H. Ardila and Van Duong Dinh.
  Communications in Partial Differential Equations, Vol. 46 (2021), No. 11, 2134-2170.


• Blow-up results for systems of nonlinear Schrödinger equation with quadratic interaction,
  joint work with Van Duong Dinh.
  Zeitschrift für angewandte Mathematik und Physik, 72 (2021), No. 5, Paper No. 178.


• Regularity results for rough solutions of the incompressible Euler equations via interpolation methods,
  joint work with Maria Colombo and Luigi De Rosa.
  Nonlinearity, 33 (2020), 4818-4836.


• Large data scattering for the Klein-Gordon equation on waveguide \(\mathbb R^d\times\mathbb T\) ,
  joint work with Lysianne Hari.
  Journal of Hyperbolic Differential Equations, Vol. 17, No. 02, pp. 355-394 (2020).


• Asymptotic dynamic for dipolar Quantum Gases below the ground state energy threshold,
  joint work with Jacopo Bellazzini.
  Journal of Functional Analysis, 277 (2019), No. 6, 1958-1998.


• Blow-up or global existence for the fractional Ginzburg-Landau equation in multi-dimensional case,
  joint work with Kazumasa Fujiwara, Vladimir Georgiev, and Tohru Ozawa.
  New Tools for Nonlinear PDEs and Applications - Trends in Mathematics (2019), Birkhäuser.


• Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential,
  joint work with Kazumasa Fujiwara, Vladimir Georgiev, and Tohru Ozawa.
  Discrete & Continuous Dynamical Systems - A, 2019, 39 (5): 2661-2678.


• Double scattering channels for 1D NLS in the energy space and its generalization to higher dimensions,
  joint work with Nicola Visciglia.
  Journal of Differential Equations, 264 (2018), No. 2, 929-958.


• The electrostatic limit for the 3D Zakharov system,
  joint work with Paolo Antonelli.
  Nonlinear Analysis, 163 (2017), 19-33.