Some similarity solutions of the Navier-Stokes equations and related topics
type: Item
instance of: scholarly article
title: Some similarity solutions of the Navier-Stokes equations and related topics
zbMATH Open document ID: 0972.35090
author: Hisashi Okamoto
author: Jinghui Zhu
published in: Taiwanese Journal of Mathematics
publication date: 2001-11-13T00:00:00Z
review text: The authors consider the equation \[ f_{txx}+ ff_{xxx}- af_x f_{xx}= \nu f_{xxxx} \] together with suitable boundary and initial conditions. The equation arises e.g. in the context of two-dimensional Navier-Stokes flow, if one tries to find a stream function of the form \(\psi(x,y,t)= yf(x,t)\). The main results concern global existence and finite time blow up of solutions for various choices of the parameters \(a\in\mathbb{R}\) and \(\nu\geq 0\).
reviewed by: Klaus Deckelnick
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 1472437
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: blow up
zbMATH Keywords: nonlocal convection
zbMATH Keywords: global existenc
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407199
OpenAlex ID: W1655384636
DOI: 10.11650/TWJM/1500407199
description: scientific article; zbMATH DE number 1472437