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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Slow decay for a linearized model of the solar wind


Author: Jack Schaeffer
Journal: Quart. Appl. Math. 70 (2012), 181-198
MSC (2000): Primary 35L60, 35Q99, 82C21, 82D10
Published electronically: September 19, 2011
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Abstract: The solar wind interacting with a magnetized obstacle is modelled with the steady Vlasov-Poisson system in the plane. The system is linearized for the (given) magnetic field of the obstacle being small. The main focus is on the rate of decay of the spatial charge density ``downwind'' of the obstacle. A special case that admits an explicit solution is presented. It is also shown that when the background particle distribution is compactly supported in velocity, that the spatial charge density cannot, in general, decay faster than $ x^{-\frac{1}{2}}_1$, where $ x_1$ is the downwind distance.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01252-2
PII: S 0033-569X(2011)01252-2
Received by editor(s): September 28, 2010
Published electronically: September 19, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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