Blow-up of a class of solutions with free boundaries for the Navier-Stokes equations
type: Item
instance of: scholarly article
title: Blow-up of a class of solutions with free boundaries for the Navier-Stokes equations
zbMATH Open document ID: 0953.35112
published in: Advances in Differential Equations
publication date: 2000-08-21T00:00:00Z
review text: A particular type of Navier-Stokes equations is considered, given in terms of two functions \(f\) and \(g\). The mechanical interpretation is a class of free-boundary problems, describing a plane jet. For \(f\), a nonlinear heat equation with a quadratic reaction term and a nonlocal term appears. This equation is ``simplified'' into a first-order Hamilton-Jacobi equation. Positive functions \(f\) are considered. The main point is to prove that the solution blows up in a finite time. An asymptotical method is used, developed in a previous paper of the authors. Some types of unstable blow-up and global patterns (with a non-generic behaviour) are considered in the last part.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 1493600
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: plane jet
zbMATH Keywords: unstable blow-up
zbMATH Keywords: global patterns
author: V. A. Galaktionov
author: Juan Luis Vázquez
reviewed by: Gelu Paşa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1493600