Self-adjoint formulation of spherically symmetric hydrodynamics
type: Item
instance of: scholarly article
title: Self-adjoint formulation of spherically symmetric hydrodynamics
zbMATH Open document ID: 0623.76074
DOI: 10.1016/0167-2789(86)90054-0
author: B. Gaffet
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: A useful extension of the self-dual formulation of one-dimensional gasdynamics to spherically symmetric compressible flow in N dimensions and to axisymmetric swirling flow is presented. A significant feature of this formulation is the fact that it is integrable in closed form. This makes it especially useful for the purpose of comparison with results from numerical calculations. The influence of the equation of state is discussed with respect to the symmetry \((T^*)\). The result corresponds to \textit{L. V. Ovsiannikov}'s analysis who pointed out the existence of such a transformation [Group analysis of differential equations (1982; Zbl 0485.58002)]. For self-similar problems the new formulation of the ordinary differential equations is very compact and leads to an algebraic general integral. This treatment of the Euler equations is suited for the investigation of conservation laws.
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 37K35
zbMATH DE Number: 4012193
zbMATH Keywords: spherical symmetry self-similar solution
zbMATH Keywords: Bäcklund transformation
zbMATH Keywords: self-dual formulation
zbMATH Keywords: one-dimensional gasdynamics
zbMATH Keywords: spherically symmetric compressible flow
zbMATH Keywords: axisymmetric swirling flow
zbMATH Keywords: Euler equations
zbMATH Keywords: conservation laws
reviewed by: Karl G. Roesner
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90054-0
OpenAlex ID: W1985527850
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description: scientific article; zbMATH DE number 4012193