4 papers
Linear stability of traveling Maxwellians for Landau equation with very soft potentials
Sanchit Chaturvedi, Jonathan Luk
Consider the Landau equation with a Coulomb potential linearized around traveling Maxwellians. We prove that the microscopic part of the linear solution decays with an inverse poly…
Linear and nonlinear phase mixing for the gravitational Vlasov-Poisson system under an external Kepler potential
Sanchit Chaturvedi, Jonathan Luk
In Newtonian gravity, a self-gravitating collisionless gas around a massive object such as a star or a planet is modeled via the Vlasov--Poisson system with an external Kepler pote…
Shock formation in 1D conservation laws II: Vanishing viscosity
John Anderson, Sanchit Chaturvedi, Cole Graham
We study the effects of weak viscosity on shock formation in 1D hyperbolic conservation laws. Given an inviscid solution that forms a nondegenerate shock, we add a small viscous re…
Shock formation in 1D conservation laws I: Inviscid structure
John Anderson, Sanchit Chaturvedi, Cole Graham
We study the stability and structure of shock formation in 1D hyperbolic conservation laws. We show that shock formation is stable near shocking simple waves: perturbations form a…