Assistant Professor • Ph.D. University of Texas at Austin, 2008
Math 319

Research interests:

PDE and Differential Geometry

Research:

PDE and Differential Geometry. In particular: fluid flows on manifolds, dispersive PDE, and equations with fractional diffusion.

Select Publications:

  • Local well-posedness for the 2 + 1 dimensional Monopole Equation. Analysis & PDE, Vol. 3, (2010), no. 2, 151-174.
  • 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.
  • Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting, with Chi Hin Chan. Dynamics of PDE 10 (2013), no.1, 43-77.
  • Lower bound for the rate of blow-up of singular solutions of the Zakharov system in R3, with James Colliander and Catherine Sulem. J. Hyperbolic Differential Equations, Vol. 10 (2013), no. 3, 523-536.
  • Topological defects in the abelian Higgs model, with Robert L. Jerrard. Discrete Contin. Dyn. Syst., Vol. 27 (2015), No. 5, 1933-1968.
  • Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space, with Chi Hin Chan. Ann. Inst. H. PoincarĂ© Anal. Non LinĂ©aire 33 (2016), no. 3, 655-698.