Publications

(with K. Cheung) Local well-posedness of stochastic nonlinear Schrödinger equations on ℝ^d with supercritical noise, preprint.

(with R. Mosincat, L. Tolomeo, Y. Wang) Global well-posedness of three-dimensional periodic stochastic nonlinear beam equations, preprint.

(with T. Oh, N. Tzvetkov) Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spaces.

(with T. Oh, Y. Wang) On the stochastic nonlinear Schrödinger equations with non-smooth additive noise, to appear in Kyoto J. Math.

(with Y. Wang) An L^p-theory for almost sure local well-posedness of the nonlinear Schrödinger equations, C. R. Math. Acad. Sci. Paris 356 (2018), no. 6, 637-643.

(with Á. Bényi, T. Oh) On the probabilistic Cauchy theory for nonlinear dispersive PDEs, Landscapes of Time-Frequency Analysis. 1-32, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, 2019.

(with Á. Bényi, T. Oh) Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ³, Trans. Amer. Math. Soc. Ser. B 6 (2019), 114-160.

(with M. Okamoto, T. Oh) On the probabilistic well-posedness of the nonlinear Schrödinger equation with non-algebraic nonlinearities, Discrete Contin. Dyn. Syst. A. 39 (2019), no. 6, 3479-3520.

(with P. Gérard, E. Lenzmann, P. Raphaël) A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line, Ann. PDE 4 (2018), no. 1, 4:7.

(with A. Choffrut) Ill-posedness of the cubic nonlinear half-wave equation and other fractional NLS on the real line, Int. Math. Res. Not. IMRN (2018), no. 3, 699-738.

(with T. Oh) A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting, Tohoku Math. J. 69 (2017), no.3, 455-481.

(with T. Oh) Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ³, J. Math. Pures Appl. 105 (2016), 342-366.

Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on ℝ^d, d = 4 and 5, J. Eur. Math. Soc. 19 (2017), 2321-2375.

(with Á. Bényi, T. Oh) On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^d, d ≥ 3, Trans. Amer. Math. Soc. Ser. B 2 (2015), 1-50.

(with Á. Bényi, T. Oh) Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS, Excursions in Harmonic Analysis, Volume 4, 3-25, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, New York, 2015.

(with R. Killip, T. Oh, M. Vişan) Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on ℝ³, Arch. Ration. Mech. Anal. 225 (2017), no. 1, 469-548.

(with R. Killip, T. Oh, M. Vişan) Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions,
Math. Res. Lett. 19 (2012), no. 5, 969-986.

First and second order approximations for a nonlinear wave equation, J. Dynam. Differential Equations, article no. 9286 (2013), 29 pp, DOI 10.1007/s10884-013-9286-5.

Soliton interaction with small Toeplitz potentials for the cubic Szegö equation on the real line, Dyn. Partial Differ. Equ. 9 (2012), no. 1, 1-27.

Explicit formula for the solutions of the the cubic Szegö equation on the real line and applications, Discrete Contin. Dyn. Syst. A 31 (2011) no. 3, 607-649.

Traveling waves for the cubic Szegö equation on the real line, Anal. PDE, 4 (2011), no. 3, 379-404.

Study of a nonlinear, non-dispersive, completely integrable equation and of its perturbations, Ph.D. thesis, advisor Prof. Patrick Gérard.