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
متن کاملar X iv : m at h - ph / 0 51 00 70 v 3 2 4 O ct 2 00 5 The Variable Coefficient Hele - Shaw Problem , Integrability and Quadrature Identities Igor
The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic PDEs with variable coefficients, emerging in a class of the free-boundary problems for viscous flows in non-homogeneous media. Such flows posses an infinite ...
متن کاملar X iv : m at h - ph / 0 51 00 70 v 2 1 9 O ct 2 00 5 The Variable Coefficient Hele - Shaw Problem , Integrability and Quadrature Identities
The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic PDEs with variable coefficients, emerging in a class of the free-boundary problems for viscous flows in non-homogeneous media. Such flows posses an infinite ...
متن کاملar X iv : m at h - ph / 0 51 00 70 v 1 1 9 O ct 2 00 5 The Variable Coefficient Hele - Shaw Problem , Integrability and Quadrature Identities
The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic PDEs with variable coefficients, emerging in a class of the free-boundary problems for viscous flows in non-homogeneous media. Such flows posses an infinite ...
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 ...
متن کامل