Steady states for a one-dimensional model of the solar wind
Author:
Jack Schaeffer
Journal:
Quart. Appl. Math. 59 (2001), 507-528
MSC:
Primary 82D10; Secondary 35F20, 35Q60, 82C21, 82C22, 85A99
DOI:
https://doi.org/10.1090/qam/1848532
MathSciNet review:
MR1848532
Full-text PDF Free Access
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Abstract: A one (space) dimensional Vlasov equation is used to model the solar wind (a collisionless plasma) as it moves past an applied magnetic field (an obstacle). The goal is to understand physically reasonable steady states for this situation. When the applied magnetic field is sufficiently small, appropriate states are constructed.
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D. Tidman and N. Krall, Shock Waves in Collisionless Plasmas, Wiley-Interscience, 1971
J. Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Differential Equations 25, 342–364 (1977)
J. Batt and K. Fabian, Stationary solutions of the relativistic Vlasov-Maxwell system of plasma physics, Chinese Ann. of Math. 14B:3, 253–278 (1993)
I. Bernstein, J. Greene, and M. Kruskal, Exact nonlinear plasma oscillations, Phys. Rev. 108, 3, 546–550 (1957)
J. W. Bruce and P. J. Giblin, Curves and Singularities, Cambridge University Press, 1984
Y. Guo, Stable magnetic equilibria in collisionless plasmas, Comm. Pure and Applied Math. 50, 891–933 (1997)
Y. Guo and C. G. Ragazzo, On steady states in a collisionless plasma, Comm. Pure and Applied Math. 49, 1145–1174 (1996)
Y. Guo and W. Strauss, Instability of periodic BGK equilibria, Comm. Pure and Applied Math. 48, 861–846 (1995)
Y. Guo and W. Strauss, Nonlinear instability of double-humped equilibria, Ann. Inst. Henri Poincaré 12, 339–352 (1995)
Y. Guo and W. Strauss, Unstable oscillatory-tail solutions, SIAM J. Math. Analysis 30, no. 5, 1076–1114 (1999)
E. Horst, On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation I, Math. Methods Appl. Sci. 3, 229–248 (1981)
E. Horst, On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation II, Math. Methods Appl. Sci. 4, 19–32 (1982)
C. S. Morawetz, Magnetohydrodynamical shock structure without collisions, Phys. Fluids 4, 988–1006 (1961)
G. Rein, A two-species plasma in the limit of large ion mass, Math. Methods Appl. Sci. 13, 159–167 (1990)
G. Rein, Nonlinear stability for the Vlasov-Poisson system—the energy-Casimir method, Math. Methods Appl. Sci. 17, 1129–1140 (1994)
G. Rein, Existence of stationary collisionless plasmas on bounded domains, Math. Methods Appl. Sci. 15, 365–374 (1992)
D. Tidman and N. Krall, Shock Waves in Collisionless Plasmas, Wiley-Interscience, 1971
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Article copyright:
© Copyright 2001
American Mathematical Society
