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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Navier-Stokes Equations and Nonlinear Function Analysis (Paperback, 2nd Revised edition)
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Navier-Stokes Equations and Nonlinear Function Analysis (Paperback, 2nd Revised edition)
Series: CBMS-NSF Regional Conference Series, v. 66
Expected to ship within 12 - 17 working days
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This second edition, like the first, attempts to arrive as simply
as possible at some central problems in the Navier Stokes equations
in the following areas: existence, uniqueness, and regularity of
solutions in space dimensions two and three; large time behaviour
of solutions and attractors; and numerical analysis of the Navier
Stokes equations. Since publication of the first edition of these
lectures in 1983, there has been extensive research in the area of
inertial manifolds for Navier Stokes equations. These developments
are addressed in a new section devoted entirely to inertial
manifolds. Inertial manifolds were first introduced under this name
in 1985 and, since then, have been systematically studied for
partial differential equations of the Navier Stokes type. Inertial
manifolds are a global version of central manifolds. When they
exist they encompass the complete dynamics of a system, reducing
the dynamics of an infinite system to that of a smooth, finite
dimensional one called the inertial system. Although the theory of
inertial manifolds for Navier Stokes equations is not complete at
this time, there is already a very interesting and significant set
of results which deserves to be known, in the hope that it will
stimulate further research in this area. These results are reported
in this edition. Part I presents the Navier Stokes equations of
viscous incompressible fluids and the main boundary value problems
usually associated with these equations. The case of the flow in a
bounded domain with periodic or zero boundary conditions is studied
and the functional setting of the equation as well as various
results on existence, uniqueness, and regularity of time dependent
solutions are given. Part II studies the behavior of solutions of
the Navier Stokes equation when t approaches infinity and attempts
to explain turbulence. Part III treats questions related to
numerical approximation. In the Appendix, which is new to the
second edition, concepts of inertial manifolds are described,
definitions and some typical results are recalled, and the
existence of inertial systems for two dimensional Navier Stokes
equations is shown.
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