On Leray's self-similar solutions of the Navier-Stokes equations satisfying local energy estimates
type: Item
instance of: scholarly article
title: On Leray's self-similar solutions of the Navier-Stokes equations satisfying local energy estimates
zbMATH Open document ID: 0916.35084
author: Tai-Peng Tsai
published in: Archive for Rational Mechanics and Analysis
publication date: 1998-11-03T00:00:00Z
full work available at URL: http://purl.umn.edu/3053
review text: The author considers self-similar solutions of the Navier-Stokes equations \[ u_t- v\Delta u+ u\nabla u+\nabla p= 0,\quad\text{div }u= 0\quad\text{in }\mathbb{R}^3\times (t_1,t_2) \] having the form \(u(x, t)= \lambda(t)\cdot U(\lambda(t)x)\), \(p(x,t)= \lambda^2(t)\cdot P(\lambda(t)x)\), where \(\lambda(t)= 1/\sqrt{2a(T- t)}\) and \(a>0\), \(T>0\). The main theorem states that any weak self-similar solution which satisfies local energy estimates in the cylinder \(B_1(0)\times(T- 1,T)\), is identically zero.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 1218195
zbMATH Keywords: weak self-similar solution
MaRDI profile type: Publication
OpenAlex ID: W2018492527
DOI: 10.1007/S002050050099
description: scientific article; zbMATH DE number 1218195