Analysis Seminar

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Global dynamics of the Kompaneets equation

Speaker: Gautam Iyer, Carnegie Mellon University

Location: Online

Date: Thursday, February 25, 2021, 11 a.m.

Synopsis:

The Kompaneets equation describes energy transport in low-density (or high temperature) plasmas where the dominant energy exchange mechanism is Compton scattering. The equation itself is a one dimensional non-linear parabolic equation with a diffusion coefficient that vanishes at the boundary. This degeneracy, combined with the nonlinearity causes an out-flux of photons with zero energy, often interpreted as a Bose--Einstein condensate. This talk will describe several results about the long time behavior of these equations including convergence to equilibrium, persistence of the condensate, sufficient conditions under which it forms, sufficient conditions under which it doesn't form and a loss formula for the mass of the condensate.

Notes:

Talk will be online, via zoom.