Communications in Mathematical Sciences

Boundary value problem for the three dimensional time periodic Vlasov-Maxwell system

M. Bostan

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Abstract

In this work we study the existence of time periodic weak solution for the three dimensional Vlasov-Maxwell system with boundary conditions. The main idea consists of using the mass, momentum and energy conservation laws which allow us to obtain a priori estimates in the case of a star-shaped bounded spatial domain. We start by constructing time periodic smooth solutions for a regularized system. The existence for the Vlasov-Maxwell system follows by weak stability under uniform estimates. These results apply for both classical and relativistic cases and for systems with several species of particles.

Article information

Source
Commun. Math. Sci., Volume 3, Number 4 (2005), 621-663.

Dates
First available in Project Euclid: 7 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.cms/1144429336

Mathematical Reviews number (MathSciNet)
MR2188688

Zentralblatt MATH identifier
1109.35109

Subjects
Primary: 35F30: Boundary value problems for nonlinear first-order equations
Secondary: 35B10: Periodic solutions 35D05 35Q60: PDEs in connection with optics and electromagnetic theory 76X05: Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 82D10: Plasmas

Citation

Bostan, M. Boundary value problem for the three dimensional time periodic Vlasov-Maxwell system. Commun. Math. Sci. 3 (2005), no. 4, 621--663. https://projecteuclid.org/euclid.cms/1144429336


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