Analysis Seminar

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Phase mixing in astrophysical plasmas with an external Kepler potential

Speaker: Sanchit Chaturvedi, New York University

Location: Warren Weaver Hall 1302

Date: Thursday, October 26, 2023, 11 a.m.

Synopsis:

In Newtonian gravity, a self-gravitating gas around a massive object such as a star or a planet is modeled via the Vlasov-Poisson equation with an external Kepler potential. The presence of this attractive potential allows for bounded trajectories along which the gas neither falls in towards the object nor escapes to infinity. We focus on this regime and prove first a linear phase mixing result in 3D outside symmetry with exact Kepler potential. Then we also prove a long-time nonlinear phase mixing result in spherical symmetry. The mechanism is phenomenologically similar to Landau damping on a torus but mathematically the situation is quite a lot more complex.

This is based on an upcoming joint work with Jonathan Luk at Stanford.