Investigation of the equation of motion of turbulent fluid under long-wave approximation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1066.76513
author: S. V. Kravchuk
publication date: 2001-03-01T00:00:00Z
Mathematics Subject Classification ID: 76F40
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1571625
zbMATH Keywords: narrow channel
zbMATH Keywords: existence
MaRDI profile type: Publication
title: Investigation of the equation of motion of turbulent fluid under long-wave approximation
published in: Visnyk. Seriya: Fizyko-Matematychni Nauky. Kyïvs'kyĭ Universytet Imeni Tarasa Shevchenka
review text: The author considers two-dimensional flow of inhomogeneous fluid in a narrow channel. The corresponding boundary value problem has the form: \(\Delta\psi= F(\psi_{y},\psi,y)\) with \(\psi=0\) on the upper boundary \(y=h_1(x)\), and \(\psi= \psi_{b}\) on the lower boundary \(y=h_2(x), \psi\to\psi_{\infty}, \psi_{x}\to0\), as \(x\to-\infty\), where \(\psi\) is the stream-function. Using long-wave approximation, the above equation is reduced to the equation \(\psi_{yy}=F(\psi_{y},\psi,y)\). The proposed method allows to establish the existence of solution, and to examine the non-uniqueness of solutions for different flow conditions.
reviewed by: Aleksandr D. Borisenko
description: scientific article