Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Theory of exact solutions for the evolution of a fluid annulus in a rotating Hele-Shaw cell


Author: Darren Crowdy
Journal: Quart. Appl. Math. 60 (2002), 11-36
MSC: Primary 76D27; Secondary 30C20, 35R35, 76E17, 76M40, 76U05
DOI: https://doi.org/10.1090/qam/1878257
MathSciNet review: MR1878257
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Abstract: Motivated by a series of recent experiments on the evolution of fluid annuli in rotating Hele-Shaw cells, this paper presents a new class of exact time-dependent solutions to a mathematical model of this nonlinear free boundary problem. For a certain class of initial conditions, the free boundary problem is reduced to the solution of a finite set of coupled nonlinear ordinary differential equations. These solutions can be explicitly studied and, despite the fact that the model problem is mathematically ill-posed, display the same qualitative features as the recent experiments. It is discussed how the present exact solutions might form an important basis for further study of the appropriately regularized model problem.


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DOI: https://doi.org/10.1090/qam/1878257
Article copyright: © Copyright 2002 American Mathematical Society


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