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.