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The Stokes operator in \(L_ R\) spaces. (English) Zbl 0471.35069

MSC:
35Q30 Navier-Stokes equations
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
47D03 Groups and semigroups of linear operators
35S15 Boundary value problems for PDEs with pseudodifferential operators
76D05 Navier-Stokes equations for incompressible viscous fluids
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[8] H. Kumano-go and M. Nagase: Lp theory of pseudo-differential operators. Proc. Japan Acad., 46, 138-142 (1970). · Zbl 0206.10404 · doi:10.3792/pja/1195520457
[9] O. A. Ladyzhenskaya: The Mathematical Theory of Viscous Incompressible Flow. Moscow (1961). · Zbl 0184.52603
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[11] F. K. G. Odqvist: Uber die Randwertaufgaben der Hydrodynamik zaher Flussigkeiten. Math. Z., 32, 329-375 (1930). · JFM 56.0713.04 · doi:10.1007/BF01194638
[12] R. Seeley: Norms and domains of the complex powers. A%. Amer. J. Math., 93, 299-309 (1971). JSTOR: · Zbl 0218.35034 · doi:10.2307/2373377 · links.jstor.org
[13] P. E. Sobolevskii: Study of Navier-Stokes equations by the methods of the theory of parabolic equations in Banach spaces. Soviet Math. Dokl., 5, 720-723 (1964). · Zbl 0201.18301
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