Pure Math: analysis of deterministic and stochastic partial differential equations including well-posedness, global existence, blow-up, scattering, solitary wave, asymptotic stability, asymptotic behavior and classification of solution, spectral theory.
Applied Math: Numerical simulation for nonlinear PDEs in various domains.
The distorted Fourier transform for the linearized Gross-Pitaevskii equation in the Hyperbolic plane. arXiv:2509.26590 with S. Shahshahani.
Equivariant stability of vortices in Manton's Chern-Simons-Schrödinger system on the hyperbolic plane. arXiv:2509.06090 with S. Shahshahani.
Construction of multi-solitary waves solution for the nonlinear Schrödinger equation outside a strictly convex obstacle. arXiv:2509.15374.
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.
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, Adv. Comput. Math., arXiv:2102.02170, with K.Yang and S.Roudenko.
Stability of vortices in the non-equivariant case for Manton's Chern-Simons-Schrödinger system on the hyperbolic plane, with S.Shahshahani.
Soliton splitting for NLS equation by double delta potentials, with J.Holmer, S.Roudenko and D.Son.
Data assimilation for 2d stochastic Navier Stokes equations, with H.Bessaih.
Stochastic elliptic-parabolic system arising in porous media with multiplicative noise, with H.Bessaih.