Publications

Preprints:

  • (with N. Rougerie, L. Tolomeo and Y. Wang) Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps, 2023. [arXiv]
  • (with N. Rougerie) Invariant Gibbs measures for 1D NLS in a trap, 2023. [arXiv]
  • (with A. Esfahani) On a system of inhomogeneous nonlinear Schrödinger equations arising in optical media with a χ(2) nonlinearity, 2022. [arXiv]

Publications:

2024

  • (with J. Bellazzini and L. Forcella) Scattering for non-radial 3D NLS with combined nonlinearities, SIAM Journal on Mathematical Analysis. Vol. 56, No. 3, pp. 3110–3143. [arXiv][Journal]

2023

  • (with M. Majdoub and T. Saanouni) Long time dynamics and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with spatial growing nonlinearity, Journal of Mathematical Physics, Vol. 64, 081509. [arXiv][Journal]
  • (with N. Rougerie and D.-T. Nguyen) Blow-up of two dimensional attractive Bose-Einstein condensates at the critical rotational speed, Annales de l’Institut Henri Poincaré C (in press), 2023. [arXiv] [Journal]
  • (with R. Carles) On stability of rotational 2D binary Bose-Einstein condensates, Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Vol. 32 (2023) no. 1, 81-124. [arXiv][Journal]

2022

  • The 3D nonlinear Schrödinger equation with a constant magnetic field revisited, Journal of Dynamics and Differential Equations, 2022. [arXiv][Journal]
  • Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed, Letter in Mathematical Physics Vol. 112 (2022), Art. No. 53. [arXiv][Journal]
  • Non-radial finite time blow-up for the fourth-order nonlinear Schrödinger equations, Applied Mathematics Letters Vol.132 (2022), 108084. [Journal]
  • (with L. Forcella) Mass-Energy threshold dynamics for dipolar Quantum Gases, Communications in Mathematical Sciences Vol. 20 (2022), no. 1, 165-200. [arXiv][Journal]
  • (with S. Keraani) A compactness result for inhomogeneous nonlinear Schrödinger equations, Nonlinear Analysis Vol. 215 (2022), 112617 (A special issue: Harmonic Analysis, Dispersive and Wave Equations). [Journal]
  • Remarks on nonlinear Schrödinger equations arising on rotational Bose-Einstein condensates, Nonlinear Analysis Vol. 214 (2022), 112587. [Journal]

2021

  • On instability of standing waves for the nonlinear Schrödinger equation with inverse-square potential, Complex Variables and Elliptic Equations Vol. 66 (2021), no. 10, 1699-1716. [arXiv] [Journal]
  • (with A. H. Ardila and L. Forcella) Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ^3 nonlinear response, Communications in Partial Differential Equations Vol. 46 (2021), no. 11, 2134-2170. [arXiv] [Journal]
  • Scattering in weighted L2 space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation, Advances in Pure and Applied Mathematics Vol. 12 (2021), no. 3, 38-72. [arXiv] [Journal]
  • (with L. Forcella) Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction, Zeitschrift für Angewandte Mathematik und Physik Vol. 72 (2021), Article No. 178. [arXiv] [Journal]
  • Non-radial scattering theory for nonlinear Schrödinger equations with potential, Nonlinear Differential Equations and Applications Vol. 28 (2021), Article No. 61. [arXiv] [Journal]
  • (with S. Keraani) Long time dynamics of non-radial solutions to inhomogeneous nonlinear Schrödinger equations, SIAM Journal on Mathematical Analysis Vol. 53 (2021), No. 4, 4765-4811. [arXiv] [Journal]
  • On nonlinear Schrödinger equations with attractive inverse-power potentials, Topological Methods in Nonlinear Analysis Vol. 57 (2021), No. 2, 489-523. [arXiv] [Journal]
  • Energy scattering for a class of inhomogeneous nonlinear Schrödinger equations in two dimensions, Journal of Hyperbolic Differential Equations Vol. 18 (2021), pp. 1-28. [arXiv] [Journal]
  • Probabilistic Cauchy theory for the mass-critical fourth-order nonlinear Schrodinger equation, Journal of Mathematical Physics Vol. 62 (2021), 031511.[pdf] [Journal]
  • Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential, Mathematische Nachrichten Vol. 294 (2021), No. 4, pp. 672-716.[pdf] [Journal]
  • On the instability of standing waves for 3D dipolar Bose-Einstein condensates, Physica D: Nonlinear Phenomena Vol. 419 (2021), ID: 132856. [pdf] [Journal]
  • Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations, Nonlinearity Vol. 34 (2021), No. 2, pp. 776-821. [pdf] [Journal]
  • Random data theory for the cubic fourth-order nonlinear Schrödinger equation, Communications on Pure and Applied Analysis Vol. 20 (2021), No. 2, pp. 651-680. [pdf] [Journal]
  • On nonlinear Schrödinger equations with repulsive inverse-power potentials, Acta Applicandae Mathematicae Vol. 174 (2021), No. 14. [pdf] [Journal]
  • Blow-up criteria for linearly damped nonlinear Schrödinger equations, Evolution Equations and Control Theory Vol. 10 (2021), No. 3, pp. 599-617. [arXiv] [Journal]
  • (with S. Keraani) The radial Sobolev-Morawetz method for the energy scattering of nonlinear Schrödinger-type equations with radial data, Discrete and Continuous Dynamical System Series S Vol. 14 (2021), No. 8, pp. 2837-2876 (Issue in memory of E. Zahnrouni). [Journal]

2020

  • Blow-up behavior of prescribed mass minimizers for nonlinear Choquard equations with singular potentials, Monatshefte für Mathematik Vol. 192 (2020), No. 3, pp. 551-589. [Journal]
  • (with S. Keraani and M. Majdoub) Long time dynamics for the focusing nonlinear Schrödinger equation with exponential nonlinearities, Dynamics of Partial Differential Equations Vol. 17 (2020), No. 4, pp. 329-360. [arXiv] [Journal]
  • A unified approach for energy scattering for focusing nonlinear Schrödinger equations, Discrete and Continuous Dynamical System Series A Vol. 40 (2020), No. 11, pp. 6441-6471. [Journal]
  • Existence and blow-up behavior of standing waves for the Gross-Pitaevskii functional with a higher order interaction, Mathematical Methods in the Applied Sciences Vol. 43 (2020), No. 12, pp. 7087-7105. [pdf] [Journal]
  • (with A. H. Ardila) Some qualitative studies of the focusing inhomogeneous Gross-Pitaevskii equation, Zeitschrift für Angewandte Mathematik und Physik Vol. 71 (2020), 71:79. [arXiv] [Journal]
  • Asymptotic behavior of constraint minimizers for the mass-critical fractional nonlinear Schrödinger equation with a sub-critical perturbation, Journal of Evolution Equations Vol. 20 (2020), No. 4, pp. 1511-1530. [Journal]
  • Existence and limiting behavior of minimizers for attractive Schrödinger-Poisson systems with periodic potentials, Mathematical Methods in the Applied Sciences Vol. 43 (2020), No. 7, pp. 4781-4797. [Journal]
  • Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schrödinger equations with periodic potentials, Proceedings of the Royal Society of Edinburgh Section A: Mathematics Vol. 150 (2020), No. 6, pp. 3252–3292. [Journal]
  • Strong instability of standing waves for a system NLS with quadratic interaction, Acta Mathematica Scientia English Series Vol. 40 (2020), pp. 515-528. [arXiv] [Journal]

2019

  • Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction, Nonlinear Analysis Vol. 190 (2019). [arXiv] [Journal]
  • (with B. Feng) On fractional nonlinear Schrödinger equation with combined power-type nonlinearities, Discrete and Contininuous Dynamical Systems Series A Vol. 39 (2019), No. 8, pp. 4565-4612. [Journal]
  • On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation, Zeitschrift für angewandte Mathematik und Physik Vol. (2019), 70:58. [arXiv] [Journal]
  • (with A. Bensouilah and M. Majdoub) Scattering in the weighted L^2-space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity, Communications on Pure and Applied Analysis Vol. 18 (2019), No. 5, pp. 2735-2755. [arXiv] [Journal]
  • Blow-up criteria for fractional nonlinear Schrödinger equations, Nonlinear Analysis: Real World Applications Vol. 48 (2019), pp. 117-140. [arXiv][Journal]
  • Energy Scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation, Journal of Evolution Equations Vol. 19 (2019), pp. 411-434. [arXiv][Journal]
  • On blowup solutions to the focusing mass-critical nonlinear fractional Schrödinger equation, Communications on Pure and Applied Analysis Vol. 18 (2019), No. 2, pp. 689-708. [arXiv] [Journal]

2018

  • (with A. Bensouilah and S. Zhu) On stability and instability of standing waves for the nonlinear Schrödinger equation with inverse-square potential, Journal of Mathematical Physics Vol. 59 (2018), 101505. [arXiv][Journal]
  • Well-posedness of nonlinear fractional Schrödinger and wave equations in Sobolev spaces, International Journal of Applied Mathematics Vol. 31 (2018), No. 4, pp. 843–525. [arXiv][Journal]
  • Global existence and blowup for a class of the focusing nonlinear Schrödinger equation with inverse-square potential, Journal of Mathematical Analysis and Applications Vol. 468 (2018), No. 1, pp. 270-303. [arXiv] [Journal]
  • Global Strichartz estimates for the fractional Schrödinger equations on asymptotically Euclidean manifolds, Journal of Functional Analysis Vol. 275 (2018), No. 8, pp. 1943-2014. [arXiv] [Journal]
  • On blowup solutions to the focusing intercritical nonlinear fourth-order Schrödinger equation, Journal of Dynamics and Differential Equations Vol. 31 (2019), pp. 1793-1823. [arXiv] [Journal]
  • On blowup solutions to the focusing L^2-supercritical nonlinear fractional Schrödinger equation, Journal of Mathematical Physics Vol. 59 (2018), 071506. [arXiv] [Journal]
  • Blowup of H^1 solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation, Nonlinear Analysis Vol. 174 (2018), pp. 169-188. [arXiv] [Journal]
  • Global existence and scattering for a class of nonlinear fourth-order Schrödinger equation below the energy space, Nonlinear Analysis Vol. 172 (2018), pp. 115-140. [arXiv] [Journal]
  • On well-posedness, regularity and ill-posedness of the nonlinear fourth-order Schrödinger equation, Bulletin of Belgium Mathematical Society Simon Stevin Vol. 25 (2018), No. 3, pp. 415-437. [arXiv] [Journal]
  • On the Cauchy problem for the nonlinear semirelativistic equation in Sobolev spaces, Discrete and Continuous Dynamical Systems Series A Vol. 38 (2018), No. 3, pp. 1127-1143. [arXiv] [Journal]
  • Global well-posedness for a L2-critical nonlinear higher-order Schrödinger equation, Journal of Mathematical Analysis Applications Vol. 458 (2018), No. 1, pp. 174-192. [arXiv] [Journal]

2017

  • On the focusing mass-critical nonlinear fourth-order Schrödinger equation below the energy space, Dynamics of Partial Differential Equations Vol. 14 (2017), No. 3, pp. 295-320. [arXiv] [Journal]
  • Strichartz estimates for the fractional Schrödinger and wave equations on compact manifolds without boundary, Journal of Differential Equations 263 (2017), No. 12, pp. 8804-8837. [arXiv] [Journal]

Unpublished papers:

  • (with S. Keraani) Energy scattering for a class of inhomogeneous biharmonic nonlinear Schrödinger equations in low dimensions, 2022. [arXiv]
  • Global existence for the defocusing mass-critical nonlinear fourth-order Schrödinger equation below the energy space, 2017. [arXiv] 
  • (with A. Bensouilah) Mass concentration and characterization of finite time blow-up solutions for the nonlinear Schrödinger equation with inverse-square potential, 2018. [arXiv]

Doctoral thesis:

  • Thesis title: Strichartz estimates and the nonlinear Schrödinger-type equations on manifolds [pdf]
  • Supervisor: Prof. Jean-Marc Bouclet