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A Theory of Exact Solutions for Plane Viscous Blobs

Crowdy, D. G. and Tanveer, S. (1998) A Theory of Exact Solutions for Plane Viscous Blobs. Journal of Nonlinear Science, 8 (3). pp. 261-279. ISSN 0938-8974.

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We present a new general theory of exact solutions for a simply connected, plane, slow viscous fluid blob with surface tension. The formulation reveals the existence of an infinite number of conserved quantities associated with the exact solutions. This new theoretical approach simplifies the calculation of concrete solutions.

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Additional Information:© 1998 Springer-Verlag New York. Received August 29, 1996; revised manuscript accepted October 3, 1997. Communicated by A. Fokas. D. G. Crowdy wishes to acknowledge advice and encouragement from Professor Philip Saffman, as well as partial support from the Department of Energy, Grant No. DE-FG03-89ER25073. S. Tanveer acknowledges support from the National Science Foundation, division of mathematical sciences. S. Tanveer also acknowledges useful discussions with Dr. F. R. Tian, in which Dr. Tian pointed out to S.T. the conserved quantities for the zero surface tension problem implicit in [8] before the present authors became aware of the paper by Cummings et al. [7].
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-89ER25073
Subject Keywords:Stokes flow, viscous drop, conservation laws, exact solutions
Issue or Number:3
Classification Code:MSC numbers. 30XX, 35XX, 76XX PAC numbers. 47.15.Gf, 47.55.Dz, 68.10.-m
Record Number:CaltechAUTHORS:20170408-142323855
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Official Citation:Crowdy, D. & Tanveer, S. J. Nonlinear Sci. (1998) 8: 261. doi:10.1007/s003329900052
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75934
Deposited By: 1Science Import
Deposited On:21 Apr 2017 03:49
Last Modified:03 Oct 2019 16:55

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