Differential and Integral Equations

Large time behavior of the relativistic Vlasov Maxwell system in low space dimension

Robert Glassey, Stephen Pankavich, and Jack Schaeffer

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When particle speeds are large the motion of a collisionless plasma is modeled by the relativistic Vlasov Maxwell system. Large time behavior of solutions which depend on one position variable and two momentum variables is considered. In the case of a single species of charge it is shown that there are solutions for which the charge density $(\rho = \int f dv)$ does not decay in time. This is in marked contrast to results for the non-relativistic Vlasov Poisson system in one space dimension. The case when two oppositely charged species are present and the net total charge is zero is also considered. In this case, it is shown that the support in the first component of momentum can grow at most as $t^{\frac{3}{4}}$.

Article information

Differential Integral Equations, Volume 23, Number 1/2 (2010), 61-77.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L60: Nonlinear first-order hyperbolic equations 35Q99: None of the above, but in this section 82C21: Dynamic continuum models (systems of particles, etc.) 82C22: Interacting particle systems [See also 60K35] 82D10: Plasmas


Glassey, Robert; Pankavich, Stephen; Schaeffer, Jack. Large time behavior of the relativistic Vlasov Maxwell system in low space dimension. Differential Integral Equations 23 (2010), no. 1/2, 61--77. https://projecteuclid.org/euclid.die/1356019387

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