Geodesic
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
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 864-876

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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: rigid body, cylindrical pipe, steady motion.
Mots-clés : viscous fluid 
@article{SEMR_2017_14_a94,
     author = {A. A. Mestnikova and V. N. Starovoitov and B. N. Starovoitova},
     title = {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},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {864--876},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a94/}
}
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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. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 864-876. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a94/