Research

Research Interest:

My main research areas are in mathematical physics and partial differential equations, studied from both pure and applied points of view.

• Pure Math: analysis of deterministic and stochastic partial differential equations including well-posedness, global existence, blow-up, scattering, solitary wave, asymptotic behavior and classification of solution.

• Applied Math: Numerical simulation for nonlinear PDEs in various domains.

Publications and Preprints:

• Threshold solutions in the focusing 3D cubic Schrödinger equation outside a strictly convex obstacle, J. Funct. Anal. 282, 5 (2022), with T.Duyckaerts and S.Roudenko.

• Construction of a solitary wave solution for the nonlinear Schrödinger equation outside a convex obstacle in the L^2-supercritical case, Discrete Contin. Dyn. Syst. Series-A (2021)

• On blow-up solutions to the nonlinear Schrödinger equation in the exterior of a convex obstacle, Dyn. Partial Differ. Eq.(2022)

• Stochastic solution of an elliptic-parabolic system arising in flow in porous media, Stoch. Dyn. 22, 3 (2022), (with H.Bessaih and C.Cohn)

• Interaction with an obstacle in the 2D focusing focusing nonlinear Schrödinger equation, to appear in Adv. Comput. Math., arXiv:2102.02170, with K.Yang and S.Roudenko.

• Construction of multi-solitary waves solution for the nonlinear Schrödinger equation outside a strictly convex obstacle.

• Iterative method for solving the fully time implicit scheme for 2D Navier-Stokes equations with additive noise, with H.Bessaih, A.Millet, V.Ginting

• Stochastic elliptic-parabolic system arising in porous media with multiplicative noise, with H.Bessaih.