Research interests
My research mainly focuses on the analysis of evolution PDEs describing physical models. More precisely, my current interests concern nonlinear dispersive PDEs, such as Schrödinger, Schrödinger-type, wave, Klein–Gordon, and Zakharov equations, together with related problems, including local and global well-posedness theory, scattering theory, formation of singularities, and dispersive PDEs on manifolds.
Papers
Below is my publication list. Click on a title to access the updated preprint of the paper.
Preprints
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NLS with mass-subcritical combined nonlinearities:
small mass \(L^2\)-scattering
Joint work with Jacopo Bellazzini and Vladimir Georgiev. (Submitted) -
Three waves interaction solitons for an energy-critical
Schrödinger system
Joint work with Xiao Luo and Xiaolong Yang. (Submitted) -
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. (Submitted) -
Invariant Gibbs dynamics for two-dimensional fractional
wave equations in negative Sobolev spaces
Joint work with Oana Pocovnicu. (Submitted)
Published Papers
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Standing waves for a Schrödinger system with three
waves interaction
Joint work with Xiao Luo, Tao Yang, and Xiaolong Yang.
Mathematische Annalen, 394 (2026), No. 2, 30. -
Mass-subcritical Half-Wave Equation with mixed
nonlinearities: existence and non-existence of ground
states and traveling waves
Joint work with Jacopo Bellazzini.
Discrete and Continuous Dynamical Systems, Vol. 53, 2026, pp. 131–145. -
Local well-posedness and blow-up in the energy space
for the 2D NLS with point interaction
Joint work with Vladimir Georgiev.
Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2025). (Published online) -
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), 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 (2021), No. 6, 229. -
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), No. 9, 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 (2020), No. 2, 355–394. -
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 and Continuous Dynamical Systems, 39 (2019), No. 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.