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Steady spatial asymptotics for the Vlasov–Poisson system
Author(s) -
Schaeffer Jack
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.354
Subject(s) - bounded function , mathematics , a priori and a posteriori , constant (computer programming) , charge (physics) , mathematical analysis , space (punctuation) , a priori estimate , positive definite matrix , infinity , mathematical physics , physics , quantum mechanics , philosophy , linguistics , eigenvalues and eigenvectors , epistemology , computer science , programming language
A collisionless plasma is modelled by the Vlasov–Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as ∣ x ∣ tends to infinity is considered. Hence, the total positive charge and the total negative charge are infinite. Smooth solutions with appropriate asymptotic behaviour were shown to exist locally in time in a previous work. This paper studies the time behaviour of the net charge and a natural quantity related to energy, and shows that neither is constant in time in general. Also, neither quantity is positive definite. When the background density is a decreasing function of ∣ v ∣, a positive definite quantity is constructed which remains bounded. A priori bounds are obtained from this. Copyright © 2003 John Wiley & Sons, Ltd.