Smooth steady solutions of the planar Vlasov-Poisson system with a magnetic obstacle

Schaeffer, Jack

doi:10.1090/S0033-569X-2014-01358-7

Author: Jack Schaeffer
Journal: Quart. Appl. Math. 72 (2014), 753-772
MSC (2010): Primary 35L60, 35Q83, 82C22, 82D10
DOI: https://doi.org/10.1090/S0033-569X-2014-01358-7
Published electronically: November 7, 2014
MathSciNet review: 3291827
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Abstract: The solar wind interacting with a magnetized obstacle is modeled with the Vlasov equation. The domain considered is a disk in the plane. Inflowing boundary conditions are given for the particle density. A magnetic field is prescribed, and the electric field is computed self consistently with potential zero on the boundary. Taking the boundary condition for the particle density to be sufficiently small, it is shown that there is a natural smooth steady solution. The speed of the inflowing plasma and the magnetic field are not size restricted.

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