Fractional Navier-Stokes equations
type: Item
instance of: scholarly article
title: Fractional Navier-Stokes equations
zbMATH Open document ID: 1414.35147
author: Jan W. Cholewa
author: Tomasz Dlotko
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2018-12-27T00:00:00Z
review text: In this paper, the authors investigate some fractional generalization of the Navier-Stokes equations. The flow domain \(\Omega \subset\mathbb{R}^N\), \(N \geq 2\) is supposed to be smooth and bounded. The authors present a detailed analysis of the existence, uniqueness, regularization and continuation properties of the solution by using the geometric theory of abstract parabolic problems. Concerning the original Navier-Stokes problem next global solutions of the Leray-Hopf type are constructed which satisfy Duhamel's integral formula, too. Finally, studying the 3-D model with zero external force they estimate a time after which the latter solution regularizes to strong solution. Furthermore, it was possible to estimate a time such that if a local strong solution exists until that time, then it exists forever. \par The paper is rather comprehensive. The proofs are mainly presented in detail and they use various modern tools from functional analysis and others like the elliptic regularity theory. The bibliography which gives a very good overview on the topic contains 52 items.
reviewed by: Jürgen Socolowsky
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 35S11
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6996817
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: abstract parabolic equations
zbMATH Keywords: initial-boundary value problems for pseudodifferential operators
MaRDI profile type: Publication
full work available at URL: dcdsb.2017149
OpenAlex ID: W2609033907
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DOI: 10.3934/DCDSB.2017149
description: scientific article; zbMATH DE number 6996817