Research
PDE, differential geometry, harmonic analysis
  1. The Meyers-Serrin Theorem on Riemannian manifolds: a survey, with Chi Hin Chan [arXiv].
  2. The Gauss formula for the Laplacian on hypersurfaces, with Chi Hin Chan [arXiv].
  3. The restriction problem on the ellipsoid, with Chi Hin Chan, Tsuyoshi Yoneda. J. Math. Anal. Appl. 527 (2023), no. 1, Paper No. 127358, 17 pp.[journal] [arXiv].
  4. Hodge decomposition of the Sobolev space H^1 on a space form of nonpositive curvature, with Chi Hin Chan, Carlos Pinilla Suarez [arXiv].
  5. Almost sure boundedness of iterates for derivative nonlinear wave equations, with Sagun Chanillo, Dana Mendelson, Andrea Nahmod, and Gigliola Staffilani. Comm. Anal. Geom. 28 (2020), no. 4, 943--977. [journal] [arXiv].
  6. Antithesis of the Stokes paradox on the hyperbolic plane, with Chi Hin Chan. J. Geom. Anal. 31 (2021), no. 5, 5033--5072. [journal] [arXiv].
  7. Asymptotic behavior of the steady Navier-Stokes equation on the hyperbolic plane, with Chi Hin Chan and Che-Kai Chen. Dynamics of Partial Differential Equations, Vol. 14, No. 3 (2017), pp. 239-270. [journal] [arXiv].
  8. The formulation of the Navier-Stokes equations on Riemannian manifolds, with Chi Hin Chan and Marcelo Disconzi. Journal of Geometry and Physics 121C (2017) pp. 335-346. [journal] [arXiv]
  9. Liouville theorem for the stationary Navier-Stokes equation on a hyperbolic space, with Chi Hin Chan. J. Math. Anal. Appl. 460 (2018), no. 1, 216--231. [journal] [arXiv]
  10. On the well-posedness of relativistic viscous fluids with non-zero vorticity, with Marcelo M. Disconzi. J. Math. Phys. 57 (2016), no. 4, 042501, 21 pp. [journal] [arXiv]
  11. Blowing up solutions to the Zakharov system for Langmuir waves, with Yuri Cher and Catherine Sulem in Laser Filamentation: Mathematical Methods and Models (CRM Series in Mathematical Physics) 2016; Springer;
  12. Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space, with Chi Hin Chan. Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 33 (2016), no. 3, 655--698. [journal] [arXiv]
  13. Topological defects in the abelian Higgs model, with Robert L. Jerrard. Discrete Contin. Dyn. Syst., Vol. 27 (2015), No. 5, 1933--1968. [journal][arXiv]
  14. An ODE for boundary layer separation on a sphere and a hyperbolic space, with Chi Hin Chan and Tsuyoshi Yoneda. Phys. D 282 (2014), 34-38. [journal][arXiv]
  15. Low regularity well-posedness for the 2D Maxwell-Klein-Gordon equation in the Coulomb gauge, with Nina Pikula. Commun. Pure Appl. Anal. 13 (2014), no. 4, 1669-1683. [journal] [arXiv]
  16. Interaction Morawetz estimate for the magnetic Schrodinger equation and applications, with James Colliander and Jeonghun Lee. Adv. Differential Equations Vol. 19 (2014), no. 9/10, 805-832.[journal]
  17. Lower bound for the rate of blow-up of singular solutions of the Zakharov system in R^3, with James Colliander and Catherine Sulem. J. Hyperbolic Differential Equations, Vol. 10 (2013), no. 3, 523-536.
  18. Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting, with Chi Hin Chan. Dynamics of PDE 10 (2013), no.1, 43-77. [journal]
  19. Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions, with Aynur Bulut, Dong Li, Nata\v sa Pavlovi\'c, Xiaoyi Zhang. Comm. Partial Differential Equations, Vol. 38 (2013), no. 4, 575-607. [arXiv]
  20. Eventual regularization of the slightly supercritical fractional Burgers equation, with Chi Hin Chan, Luis Silvestre. Discrete Contin. Dyn. Syst., Vol. 27 (2010), no. 2, 847-861.
  21. Regularity of solutions for the critical N-dimensional Burgers' equation, with Chi Hin Chan. Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, Vol. 27 (2010), no. 2, 471-501.
  22. Local well-posedness for the $2+1$ dimensional Monopole Equation. Analysis & PDE, Vol. 3, (2010), no. 2, 151-174.
Expository