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Published in:
2005 | OriginalPaper | Chapter
Very Weak Solutions of Stationary and Instationary Navier-Stokes Equations with Nonhomogeneous Data
Authors : Reinhard Farwig, Giovanni P. Galdi, Hermann Sohr
Published in: Nonlinear Elliptic and Parabolic Problems
Publisher: Birkhäuser Basel
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We investigate several aspects of
very weak solutions u
to stationary and nonstationary Navier-Stokes equations in a bounded domain Ω
$$ \subseteq $$
ℝ
3
. This notion was introduced by Amann [3], [4] for the nonstationary case with nonhomogeneous boundary data
u
|
ϕΩ
=
g
leading to a new and very large solution class. Here we are mainly interested to investigate the ‘largest possible’ class for the more general problem with arbitrary divergence
k
= div
u
, boundary data
g
=
u
|
ϕΩ
. and an external force
f
, as weak as possible. In principle, we will follow Amann’s approach.