Research Interests

Analysis and PDEs arising in fluid and gas dynamics, kinetic theory, plasma physics, and astrophysics

  • Moving boundary value problems for compressible Euler and Navier-Stokes equations
  • Stability theory for compressible fluids driven by gravity
  • Singularities in fluid and gas dynamics
  • Hydrodynamic limits from the kinetic equations


Selected Recent Publications
  • Naked singularities in the Einstein-Euler system (with Yan Guo and Mahir Hadzic), Annals of PDE (2023) 9:4
  • Incompressible Euler limit from Boltzmann equation with Diffuse Boundary Condition for Analytic data (with Chanwoo Kim), Annals of PDE (2021) 7:22
  • Continued Gravitational Collapse for Newtonian Stars (with Yan Guo and Mahir Hadzic), Archive for Rational Mechanics and Analysis 239 (2021), 431-552
  • Expanding large global solutions of the equations of compressible fluid mechanics (with Mahir Hadzic), Inventiones mathematicae 214 (2018), no. 3, 1205-1266
  • Nonlinear stability of expanding star solutions in the radially-symmetric mass-critical Euler-Poisson system (with Mahir Hadzic), Communications on Pure and Applied Mathematics 71 (2018), no.5, 827-891

A complete list can be found at Publications.


Teaching at USC


2019 USC Summer School on Mathematical Fluids (May 20 – May 24 2019)


USC Summer School on Mathematical Fluids (May 22 – May 26 2017)