New applications of quantum algebraically integrable systems in fluid dynamics

被引：0

作者：

Anne Boutet de Monvel

Igor Loutsenko

Oksana Yermolayeva

机构：

[1] UPD Paris-VII,Institut de Mathématiques de Jussieu

[2] UPMC Paris-VI,Institut Henri Poincaré

来源：

Analysis and Mathematical Physics | 2013年 / 3卷

关键词：

Free boundary problems; Hele-Shaw problem; Laplacian growth; Filtration flows; Integrable systems; 35J08 Green’s functions; 35J10 Schrödinger operator; 35N10 Overdetermined systems with variable coefficients; 35J57 Boundary value problems for second-order elliptic systems; 35R35 Free boundary problems; 76S05 Flows in porous media; filtration; 76D27 Other free-boundary flows; Hele-Shaw flows;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Rational quantum algebraically integrable systems are non-trivial generalizations of Laplacian operators to the case of elliptic operators with variable coefficients. We study corresponding extensions of Laplacian growth connected with algebraically integrable systems, describing viscous free-boundary flows in non-homogenous media. We introduce a class of planar flows related with application of Adler-Moser polynomials and construct solutions for higher-dimensional cases, where the conformal mapping technique is unavailable.

引用

页码：277 / 294

页数：17

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