Nonlinear Boltzmann Equation Solutions and Applications to Fluid Dynamics

1995 ◽  
Vol 48 (12) ◽  
pp. 777-794 ◽  
Author(s):  
N. Bellomo ◽  
P. LeTallec ◽  
B. Perthame
Keyword(s):  
Fluid Dynamics ◽  
Boltzmann Equation ◽  
Qualitative Analysis ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Mathematical Formulation ◽  
Nonlinear Boltzmann Equation ◽  
Computational Aspects ◽  
Formulation Of Problems

This paper provides a review of the mathematical results on the solution of the nonlinear Boltzmann equation. The survey deals both with analytical and computational aspects: Mathematical formulation of problems, initial and/or boundary value problems, a survey of the qualitative analysis of solutions, and computational treatment of fluid dynamical problems. A discussion of some problems deserving further study concludes this work.

RADIATION FROM SOURCES IMMERSED IN COMPRESSIBLE PLASMA MEDIA

1964 ◽  
Vol 42 (9) ◽  
pp. 1760-1780 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Fluid Dynamics ◽  
Boundary Value Problems ◽  
Cold Plasma ◽  
Boundary Value ◽  
Continuum Theory ◽  
Acoustic Velocity ◽  
Compressible Plasma ◽  
Dielectric Cavity ◽  
Approach Zero ◽  
Electron Acoustic

Boundary value problems involving dielectric and compressible plasma media are considered. The geometrical configurations are idealized to the extent that Maxwell's equations, when combined with continuum theory of fluid dynamics, are separable. The specific problems considered are motivated by a need to understand radiation of sources immersed in compressible isotropic ionized media. Various results for cold plasma configurations are recovered when the (electron) acoustic velocity is allowed to approach zero. Some attention is given to phenomena related to the resonance in the dielectric cavity which contains the sources. In particular, it is shown that the resonant conditions are modified appreciably by the finite compressibility of the surrounding plasma.

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