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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 397, Pages 73–88
(Mi znsl4668)
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This article is cited in 4 scientific papers (total in 4 papers)
Estimates of deviations from exact solution of the Stokes problem in the vorticity-velocity-pressure formulation
A. Mikhaylov, S. Repin St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
Vorticity-velocity-pressure formulation for the stationary Stokes problem in 2D is considered. We analyze the corresponding generalized formulation, establish sufficient conditions that guarantee existence of the generalized solution and deduce estimates of the difference between the exact solution (i.e., exact velocity, vorticity, and pressure) and an arbitrary approximating function (velocity, vorticity, pressure) that belongs to the corresponding functional class and satisfies the boundary conditions. For this purpose we use the method suggested in [10, 12], which is based on transformations of the integral identity that defines the corresponding generalized solution.
Key words and phrases:
Stokes problem, viscous incompressible fluids, estimates of deviations from exact solutions.
Received: 03.11.2011
Citation:
A. Mikhaylov, S. Repin, “Estimates of deviations from exact solution of the Stokes problem in the vorticity-velocity-pressure formulation”, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Zap. Nauchn. Sem. POMI, 397, POMI, St. Petersburg, 2011, 73–88; J. Math. Sci. (N. Y.), 185:5 (2012), 698–706
Linking options:
https://www.mathnet.ru/eng/znsl4668 https://www.mathnet.ru/eng/znsl/v397/p73
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Abstract page: | 226 | Full-text PDF : | 53 | References: | 40 |
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