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The string equation for polynomials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-3125-3030
2018 (English)In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 8, no 4, p. 637-653Article in journal (Refereed) Published
Abstract [en]

For conformal maps defined in the unit disk one can define a certain Poisson bracket that involves the harmonic moments of the image domain. When this bracket is applied to the conformal map itself together with its conformally reflected map the result is identically one. This is called the string equation, and it is closely connected to the governing equation, the Polubarinova–Galin equation, for the evolution of a Hele-Shaw blob of a viscous fluid (or, by another name, Laplacian growth). In the present paper we show that the string equation makes sense and holds for general polynomials.

Place, publisher, year, edition, pages
Springer Basel , 2018. Vol. 8, no 4, p. 637-653
Keywords [en]
harmonic moment, Hele-Shaw flow, Laplacian growth, Poisson bracket, Polubarinova–Galin equation, resultant, String equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-247089DOI: 10.1007/s13324-018-0239-3ISI: 000451394300010Scopus ID: 2-s2.0-85057449868OAI: oai:DiVA.org:kth-247089DiVA, id: diva2:1302285
Note

QC 20190404

Available from: 2019-04-04 Created: 2019-04-04 Last updated: 2019-04-04Bibliographically approved

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Gustafsson, Björn

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