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Derivation of the Ion equation

Banff International Research Station for Mathematical Innovation and Discovery

(Joint work with Y. Guo, E. Grenier and M. Suzuki) We consider the 2 fluid Euler-Poisson equation in 3d space and show that, when the mass of electron tends to 0, the solutions can be well approximated by the strong limit which solves the (1 fluid) Euler-Poisson equation for ions and an initial layer which disperses the excess electron density and velocity in short time. This is a singular limit, somewhat akin to the low-Mach number problem studied by Klainerman-Majda, Ukai and Metivier-Schochet, but in this case, the dispersive layer comes from a quasilinear equation involving coefficients depending on space and time (in fact depending on the strong limit), and the analysis relies on a local energy decay.

Mathematics; Partial differential equations; Fourier analysis

video/mp4

Author affiliation: Brown University

2020-01-01

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73041

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/