Monniaux, Sylvie Navier-Stokes equations in arbitrary domains: the Fujita-Kato scheme. (English) Zbl 1126.35044 Math. Res. Lett. 13, No. 2-3, 455-461 (2006). 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. Reviewer: Klaus Deckelnick (Magdeburg) Cited in 7 Documents 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 Keywords:mild solution; Stokes operator; local strong solution; Fujita-Kato method PDFBibTeX XMLCite \textit{S. Monniaux}, Math. Res. Lett. 13, No. 2--3, 455--461 (2006; Zbl 1126.35044) Full Text: DOI arXiv