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Navier-Stokes equations in arbitrary domains: the Fujita-Kato scheme. (English) Zbl 1126.35044

The author considers the instationary Navier-Stokes equations in an arbitrary open set \(\Omega\subset\mathbb{R}^3\). On the basis of a suitable definition of the Stokes operator which avoids any assumption on the regularity of \(\partial \Omega\) she constructs a local strong solution of the Navier-Stokes system via the Fujita-Kato method.

MSC:

35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
35A15 Variational methods applied to PDEs
35K90 Abstract parabolic equations
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