Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


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
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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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Additional Information

Jack Schaeffer
Affiliation: Department of Mathematics Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email: js5m@andrew.cmu.edu

DOI: https://doi.org/10.1090/S0033-569X-2014-01358-7
Received by editor(s): January 15, 2013
Published electronically: November 7, 2014
Article copyright: © Copyright 2014 Brown University

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