2 00 7 Regularization of Hele - Shaw flows , multiscaling expansions and the Painlevé I equation ∗
نویسنده
چکیده
Critical processes of ideal integrable models of Hele-Shaw flows are considered. A regularization method based on multiscaling expansions of solutions of the KdV and Toda hierarchies characterized by string equations is proposed. Examples are exhibited in which the tritronquée solution of the Painlevé-I equation turns out to provide the leading term of the regularization
منابع مشابه
Regularization of Hele-shaw Flows, Multiscaling Expansions and the Painlevé I Equation *
Critical processes of ideal integrable models of Hele-Shaw flows are considered. A regularization method based on multiscaling expansions of solutions of the KdV and Toda hierarchies characterized by string equations is proposed. Examples are exhibited in which the tritronquée solution of the Painlevé-I equation turns out to provide the leading term of the regularization
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متن کاملConformal and Potential Analysis in Hele-Shaw cells
Preface One of the most influential works in Fluid Dynamics at the edge of the 19-th century was a short paper [130] written by Henry Selby Hele-Shaw (1854–1941). There Hele-Shaw first described his famous cell that became a subject of deep investigation only more than 50 years later. A Hele-Shaw cell is a device for investigating two-dimensional flow of a viscous fluid in a narrow gap between ...
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تاریخ انتشار 2013