Research Interest:
I am currently interested in:

 Strichartz estimates for the linear Schrodingertype equations (fractional Schrodinger equation, half wave equation, higherorder Schrodinger equation) on manifolds.
 Local and global wellposedness, blowup, scattering, stability and instability of standing waves for the nonlinear fractional Schrodinger equation, nonlinear half wave equation, nonlinear fourthorder Schrodinger equation, inhomogeneous nonlinear Schrodinger equation, nonlinear Schrodinger equation with inversesquare potential and system of nonlinear Schrodinger equations.
 Mass concentration of prescribed mass minimizers for the energy functional related to nonlinear Schrodinger equations, nonlinear Hartree equations, fractional nonlinear Schrodinger equations and SchrodingerPoisson systems.
Publications:
2019
 Existence, nonexistence and blowup behavior of minimizers for the masscritical fractional nonlinear Schrodinger equations with periodic potentials, to appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics. [pdf]
 Strong instability of standing waves for a system NLS with quadratic interaction, to appear in Acta Mathematica Scientia English Series. [arXiv]
 Existence, stability of standing waves and the characterization of finite time blowup solutions for a system NLS with quadratic interaction, Nonlinear Anal. 190 (2019). [arXiv] [Journal]
 (with B. Feng) On fractional nonlinear Schrodinger equation with combined powertype nonlinearities, Discrete Contin. Dyn. Syst. 39 (2019), No. 8, pp. 45654612. [pdf] [Journal]
 On instability of standing waves for the masssupercritical fractional nonlinear Schrodinger equation, Z. Angew. Math. Phys. (2019) 70:58. [arXiv] [Journal]
 (with A. Bensouilah and M. Majdoub) Scattering in the weighted L^2space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity, Commun. Pure Appl. Anal. 18 (2019), No. 5, pp. 27352755. [arXiv] [Journal]
 Blowup criteria for fractional nonlinear Schrodinger equations, Nonlinear Anal. Real World Appl. 48 (2019), pp. 117140. [arXiv][Journal]
 Energy Scattering for a class of the defocusing inhomogeneous nonlinear Schrodinger equation, J. Evol. Equ. 2019, pp. 124. [arXiv][Journal]
 On blowup solutions to the focusing masscritical nonlinear fractional Schrodinger equation, Commun. Pure Appl. Anal. 18 (2019), No. 2, pp. 689708. [arXiv] [Journal]
2018
 (with A. Bensouilah and S. Zhu) On stability and instability of standing waves for the nonlinear Schrodinger equation with inversesquare potential, J. Math. Phys. 59 (2018), 101505. [arXiv][Journal]
 Wellposedness of nonlinear fractional Schrodinger and wave equations in Sobolev spaces, Int. J. Appl. Math. 31 (2018), No. 4, pp. 843–525. [arXiv][Journal]
 Global existence and blowup for a class of the focusing nonlinear Schrodinger equation with inversesquare potential, J. Math. Anal. Appl. 468 (2018), No. 1, pp. 270303. [arXiv] [Journal]
 Global Strichartz estimates for the fractional Schrodinger equations on asymptotically Euclidean manifolds, J. Funct. Anal. 275 (2018), No. 8, pp. 19432014. [arXiv] [Journal]
 On blowup solutions to the focusing intercritical nonlinear fourthorder Schrodinger equation, J. Dynam. Differential Equations 2018 (online first). [arXiv] [Journal]
 On blowup solutions to the focusing L^2supercritical nonlinear fractional Schrodinger equation, J. Math. Phys. 59 (2018), 071506. [arXiv] [Journal]
 Blowup of H^1 solutions for a class of the focusing inhomogeneous nonlinear Schrodinger equation, Nonlinear Anal. 174 (2018), pp. 169188. [arXiv] [Journal]
 Global existence and scattering for a class of nonlinear fourthorder Schrodinger equation below the energy space, Nonlinear Anal. 172 (2018), pp. 115140. [arXiv] [Journal]
 On wellposedness, regularity and illposedness of the nonlinear fourthorder Schrodinger equation, Bull. Belg. Math. Soc. Simon Stevin, 25 (2018), No. 3, pp. 415437. [arXiv] [Journal]
 On the Cauchy problem for the nonlinear semirelativistic equation in Sobolev spaces, Discrete Contin. Dyn. Syst. 38 (2018), No. 3, pp. 11271143. [arXiv] [Journal]
 Global wellposedness for a L2critical nonlinear higherorder Schrodinger equation, J. Math. Anal. Appl. 458 (2018), No. 1, pp. 174192. [arXiv] [Journal]
2017
 On the focusing masscritical nonlinear fourthorder Schrodinger equation below the energy space, Dyn. Partial Differ. Equ. 14 (2017), No. 3, pp. 295320. [arXiv] [Journal]
 Strichartz estimates for the fractional Schrodinger and wave equations on compact manifolds without boundary, J. Differential Equations 263 (2017), No. 12, pp. 88048837. [arXiv] [Journal]
Preprints:
 (with S. Keraani and M. Majdoub) Long time dynamics for the focusing nonlinear Schrodinger equation with exponential nonlinearities, submitted, 2019.
 Global dynamics for a class of inhomogeneous nonlinear Schrodinger equations with potential, 2019. [arXiv]
 Energy scattering for a class of inhomogeneous nonlinear Schrodinger equations in two dimensions, 2019. [arXiv]
 Existence and blowup behavior of standing waves for the GrossPitaevskii functional with a higher order interaction, 2019. [pdf]
 On nonlinear Schrodinger equations with attractive inversepower potentials, 2019. [arXiv]
 (with A. H. Ardila) Some qualitative studies of the focusing inhomogeneous GrossPitaevskii equation, 2019. [arXiv]
 On nonlinear Schrodinger equations with repulsive inversepower potentials, submitted, 2018. [arXiv]
 On instability of standing waves for the nonlinear Schrödinger equation with inversesquare potential, submitted, 2018. [arXiv]

Scattering in weighted L2 space for a class of the defocusing inhomogeneous nonlinear Schrodinger equation, submitted, 2017. [arXiv]
Unpublished papers:
 Global existence for the defocusing masscritical nonlinear fourthorder Schrodinger equation below the energy space, 2017. [arXiv]
 (with A. Bensouilah) Mass concentration and characterization of finite time blowup solutions for the nonlinear Schrodinger equation with inversesquare potential, 2018. [arXiv]
Doctoral thesis:
 Thesis title: Strichartz estimates and the nonlinear Schrodingertype equations on manifolds [pdf]
 Supervisor: Prof. JeanMarc Bouclet