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Summary: Nonhomogeneous Navier-Stokes equations
with integrable low-regularity data
Herbert Amann
Dedicated to O.A. Ladyzhenskaya on the occasion of her 80 th birthday
On the basis of semigroup and maximal regularity techniques, we derive optimal
existence and uniqueness results for the Navier-Stokes equations in spaces of low
regularity.
Introduction and main results
Throughout this paper, unless explicitly stated
otherwise,
is a subdomain
of R 3 having a nonempty compact smooth boundary, , lying locally on one side
of
We study solvability questions for the nonhomogeneous nonstationary
incompressible Navier-Stokes equations
r v
@ t v + (v r)v v
= 0
= r + f
in
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