This book offers an essential introduction to the mathematical theory of compressible viscous
fluids. The main goal is to present analytical methods from the perspective of their numerical
applications. Accordingly we introduce the principal theoretical tools needed to handle
well-posedness of the underlying Navier-Stokes system study the problems of sequential
stability and lastly construct solutions by means of an implicit numerical scheme. Offering
a unique contribution - by exploring in detail the synergy of analytical and numerical methods
- the book offers a valuable resource for graduate students in mathematics and researchers
working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that
are closely connected to real-world applications and is also an important part of the theory of
partial differential equations and numerical analysis in general. This book highlights the fact
that numerical and mathematical analysis are not two separate fields of mathematics. It will
help graduate students and researchers to not only better understand problems in mathematical
compressible fluid mechanics but also to learn something from the field of mathematical and
numerical analysis and to see the connections between the two worlds. Potential readers should
possess a good command of the basic tools of functional analysis and partial differential
equations including the function spaces of Sobolev type.
