This monograph is dedicated to the derivation and analysis of
fluid models occurring in plasma physics. It focuses on models
involving quasi-neutrality approximation, problems related to laser
propagation in a plasma, and coupling plasma waves and
electromagnetic waves. Applied mathematicians will find a
stimulating introduction to the world of plasma physics and a few
open problems that are mathematically rich. Physicists who may be
overwhelmed by the abundance of models and uncertain of their
underlying assumptions will find basic mathematical properties of
the related systems of partial differential equations. A planned
second volume will be devoted to kinetic models.
First and foremost, this book mathematically derives certain
common fluid models from more general models. Although some of
these derivations may be well known to physicists, it is important
to highlight the assumptions underlying the derivations and to
realize that some seemingly simple approximations turn out to be
more complicated than they look. Such approximations are justified
using asymptotic analysis wherever possible. Furthermore, efficient
simulations of multi-dimensional models require precise statements
of the related systems of partial differential equations along with
appropriate boundary conditions. Some mathematical properties of
these systems are presented which offer hints to those using
numerical methods, although numerics is not the primary focus of
the book.
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