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The Navier-Stokes Equations - An Elementary Functional Analytic Approach (Paperback, Reprint of the 1st edition 2001 by Birkhauser Verlag, Switzerland)
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The Navier-Stokes Equations - An Elementary Functional Analytic Approach (Paperback, Reprint of the 1st edition 2001 by Birkhauser Verlag, Switzerland)
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The primary objective of this monograph is to develop an elementary
and se-
containedapproachtothemathematicaltheoryofaviscousincompressible?uid
n in a domain ? of the Euclidean spaceR, described by the equations
of Navier- Stokes. The book is mainly directed to students familiar
with basic functional analytic tools in Hilbert and Banach spaces.
However, for readers' convenience, in the ?rst two chapters we
collect, without proof some fundamental properties of Sobolev
spaces, distributions, operators, etc. Another important objective
is to formulate the theory for a completely general domain ?. In
particular, the theory applies to arbitrary unbounded, non-smooth
domains. For this reason, in the nonlinear case, we have to
restrict ourselves to space dimensions n=2,3 that are also most
signi?cant from the physical point of view. For mathematical
generality, we will develop the l- earized theory for all n? 2.
Although the functional-analytic approach developed here is, in
principle, known to specialists, its systematic treatment is not
available, and even the
diverseaspectsavailablearespreadoutintheliterature.However,
theliterature is very wide, and I did not even try to include a
full list of related papers, also because this could be confusing
for the student. In this regard, I would like to apologize for not
quoting all the works that, directly or indirectly, have inspired
this monograph.
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