Jonathan Luk

Improved decay for solutions to the linear wave equation on a Schwarzschild black hole

We prove that sufficiently regular solutions to the wave equation

A fully anisotropic mechanism for formation of trapped surfaces in vacuum

{\square_g\phi=0}

Strichartz Estimates and Moment Bounds for the Relativistic Vlasov–Maxwell System

on the exterior of the Schwarzschild black hole obey the estimates

Shock formation in solutions to the 2 D compressible Euler equations in the presence of non-zero vorticity

{|\phi|\leq C_\delta v_+^{-\frac{3}{2}+\delta}}

Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system II. Continuation criteria in the 3D case

and