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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 362, Pages 120–152
(Mi znsl2195)
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This article is cited in 2 scientific papers (total in 2 papers)
Special global regular solutions to the Navier–Stokes equations
W. M. Zajączkowskiab a Institute of Mathematics of the Polish Academy of Sciences
b Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology
Abstract:
We present the existence results of global regular solutions to the Navier–Stokes equations which are close either to two-dimensional or to axially-symmetric solutions. We assume the slip-boundary conditions. Moreover, the considered domains are either cylindrical or axially symmetric. We examine problems with and without inflow-outflow. All proofs can be divided into two steps: 1. long time existence by either the Leray–Schauder fixed point theorem or the method of successive approximations, 2. global existence by prolongation of the local solution with respect to time. Bibl. – 32 titles.
Received: 27.11.2008
Citation:
W. M. Zajączkowski, “Special global regular solutions to the Navier–Stokes equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Zap. Nauchn. Sem. POMI, 362, POMI, St. Petersburg, 2008, 120–152; J. Math. Sci. (N. Y.), 159:4 (2009), 452–471
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https://www.mathnet.ru/eng/znsl2195 https://www.mathnet.ru/eng/znsl/v362/p120
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Abstract page: | 205 | Full-text PDF : | 62 | References: | 50 |
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