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Differentical equations, dynamical systems and optimal control
The steady problem of the motion of a rigid ball in a Stokes–Poiseuille flow: differentiability of the solution with respect to the ball position
A. A. Mestnikovaa, V. N. Starovoitovba, B. N. Starovoitovaa a Lavrentyev Institute of Hydrodynamics,
pr. Lavrentyeva, 15
630090, Novosibirsk, Russia
b Novosibirsk State University,
ul. Pirogova, 2
630090, Novosibirsk, Russia
Abstract:
This paper deals with the steady problem of the motion of a rigid body in a viscous incompressible fluid that fills a cylindrical domain. The fluid flow is governed by the Stokes equation and tends to Poiseuille flow at infinity. The body is a ball that moves according to the laws of classical mechanics. The unique solvability of this problem was proved in an earlier work of the authors. Here, the differentiability of the solution in the function space $L^2$ with respect to the position of the ball is established.
Keywords:
viscous fluid, rigid body, cylindrical pipe, steady motion.
Received May 2, 2017, published September 14, 2017
Citation:
A. A. Mestnikova, V. N. Starovoitov, B. N. Starovoitova, “The steady problem of the motion of a rigid ball in a Stokes–Poiseuille flow: differentiability of the solution with respect to the ball position”, Sib. Èlektron. Mat. Izv., 14 (2017), 864–876
Linking options:
https://www.mathnet.ru/eng/semr830 https://www.mathnet.ru/eng/semr/v14/p864
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Abstract page: | 133 | Full-text PDF : | 38 | References: | 28 |
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