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Fundamental Directions in Mathematical Fluid Mechanics (Hardcover, 2000 ed.)
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Fundamental Directions in Mathematical Fluid Mechanics (Hardcover, 2000 ed.)
Series: Advances in Mathematical Fluid Mechanics
Expected to ship within 10 - 15 working days
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This set of six papers, written by eminent experts in the field, is
concerned with that part of fluid mechanics that seeks its
foundation in the rigorous mathematical treatment of the
Navier-Stokes equations. In particular, an overview is given on
state of research regarding the global existence of smooth
solutions, for which uniqueness and continuous dependence on the
data can be proven. Then, the book moves on to a discussion of
recent developments of the finite element Galerkin method, with an
emphasis on a priori and a posteriori error estimation and adaptive
mesh refinement. A further article elaborates on spectral Galerkin
methods and their extension to domains with complicated geometries
by employing the techniques of domain decomposition. The rigorous
explanation of bifurcation phenomena in fluids has long been a
central topic in the theory of Navier-Stokes equations. Here,
bifurcation theory is introduced in a general setting that is
particularly convenient for application to such problems. Finally,
the extension of Navier-Stokes theory to compressible viscous
flows, studied in two more papers, opens up a fascinating panorama
of theoretical and numerical problems. While some of the
contributions are expository, others primarily present new results
within a wider context and fuller exposition than is usual for
research papers. The book is meant to introduce researchers and
advanced students to the research level on some of the most
important topics of the field.
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