Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere

Details Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere

2000-12-14

arxiv.org/abs/math-ph/0012027v2

Electronic Journal of Differential Equations, Vol 2001(2001), No. 62, pp. 1-17

Physics

Mathematical Physics

17 pages, 2 figures. Fixed typographical errors, included an appendix to clarify the derivation

Scientific paper

We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem.

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