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Zbl 1044.35053
Hillairet, M.; Serre, D.
Chute stationnaire d'un solide dans un fluide visqueux incompressible le long d'un plan incliné. (Free steady fall of a solid in a fluid, along a ramp). (French)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 20, No. 5, 779-803 (2003). ISSN 0294-1449

Summary: The three-dimensional space is filled by a Newtonian fluid above a fixed ramp. A spherical solid body falls in the fluid under the action of the gravity. We are interested in permanent regimes, in which gravity and the action of the stress tensor of the fluid on the solid compensate. We prove that there exist such regimes, in which some parameters are given (including the gravity, the velocity of the solid and its distance to the ramp), but others, such as the mass and the angular velocity, are determined by the motion.\par We encounter two main difficulties. First in establishing a (non-explicit) a priori estimate. Last, because we are not able to convert the problem into the search of a zero of some outgoing vector field in a ball.

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory
76D27 Other free-boundary flows; Hele-Shaw flows

Keywords: existence; Newtonian fluid; permanent regimes; a priori estimate

Cited in: Zbl 1229.35183

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