Global Smooth Ion Dynamics in the Euler-Poisson System

• Published in: Communications in mathematical physics Vol. 303; no. 1; pp. 89 - 125
• Main Authors: Guo, Yan, Pausader, Benoit
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-04-2011; Springer
• Subjects: Classical and Quantum Gravitation; Complex Systems; Exact sciences and technology; Mathematical and Computational Physics; Mathematical methods in physics; Mathematical Physics; Other topics in mathematical methods in physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical; Commun Math Phys; Global Solution; Zakharov Equation; Poisson System; Multiplier Theorem; Compressible fluid; Smooth dynamics; Fluid dynamics; Dynamic model; Electric fields; Global solution; Mathematical physics
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-011-1193-1

A fundamental two-fluid model for describing dynamics of a plasma is the Euler-Poisson system, in which compressible ion and electron fluids interact with their self-consistent electrostatic force. Global smooth electron dynamics were constructed in Guo (Commun Math Phys 195:249–265,
1998
) due to dispersive effect of the electric field. In this paper, we construct global smooth irrotational solutions with small amplitude for ion dynamics in the Euler-Poisson system.