Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere
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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.
17 pages, 2 figures. Fixed typographical errors, included an appendix to clarify the derivation
17 pages, 2 figures. Fixed typographical errors, included an appendix to clarify the derivation