Research

Grants and Funds:

  • NSF Grant DMS-1853002, DMS-2104775
  • Simons Collaboration Grant for Mathematician (pre-award)

Research Interest

Partial differential equations; numerical analysis; mathematical physics.

Kinetic Theory

  • Hydrodynamic Limits with Boundary Effects
  • Neutron Transport Equation and Radiative Transfer Equation
  • Relativistic and Quantum Boltzmann/Landau Equation
  • Vlasov-Poisson/Maxwell System
  • Vlasov-Poisson/Maxwell-Boltzmann/Landau System

Fluid Mechanics

  • Viscous Surface Wave
  • Surfactant-Driven Surface Wave
  • Droplet with Contact Line
  • Hydrodynamic Stability

Solid Mechanics

  • Dislocation of Crystals/Quasi-Crystals
  • Free Energy with Variational Methods

Dispersive Equations

  • Korteweg–De Vries Equation
  • Nonlinear Schrodinger Equation/Modified Korteweg–De Vries Equation
  • Continuum Limit of Ablowitz-Ladik Model

Numerical Analysis

  • Discontinuous Galerkin Method
  • Asymptotic-Preserving Schemes and Stiff Problems