My current research is in the area of nonlinear partial differential equations, motivated by the problems in mathematical physics.
Rotating quantum fluids with self-gravitation (with C. Sparber). (2025), in preparation.
Threshold solutions for the Hartree equation (with S. Roudenko). (2025), submitted. arXiv
Self-bound vortex states in nonlinear Schrödinger equations with LHY correction (with C. Sparber). Nonlinear Differ. Equ. Appl., 30, (2022), Article No. 14. arXiv
Well-posedness in weighted spaces for the generalized Hartree equation with p < 2 (with O. Riaño and S. Roudenko). Commun. Contemp. Math., 24(9), (2022), 51 pp. arXiv
Global behavior of solutions to the focusing generalized Hartree equation (with S. Roudenko). Michigan Math. J., 71(3), (2022), 619-672. arXiv
Scattering below the ground state for the 2d radial nonlinear Schrödinger equation (with B. Dodson and J. Murphy). Proc. Amer. Math. Soc., 148(4), (2020), 1653-1663. arXiv
Well-posedness and blow-up properties for the generalized Hartree equation (with S. Roudenko). J. Hyperbolic Differ. Equ., 17(4), (2020), 727-763. arXiv
On the focusing generalized Hartree equations (with S. Roudenko and K. Yang). Math. in Appl. Sci. and Eng., 1(4), (2020), 383-402.
Scattering of radial data in the focusing NLS and generalized Hartree equation. Discrete Contin. Dyn. Syst. Series-A, 39 (2019), 6643-6668. arXiv
Exponential bases on two dimensional trapezoids (with L. De Carli), Proc. Amer. Math. Soc. 143(7), (2015), 2893-2903. arXiv