UZH-Logo

Maintenance Infos

Remarks on the strong solvability of the Navier-Stokes equations


Amann, H (2001). Remarks on the strong solvability of the Navier-Stokes equations. Functional Differential Equations, 8(1-2):3-9.

Abstract

Throughout this note m≥3 and either Ω=Rm, or Ω is a half-space of Rm, or Ω is a smooth domain in Rm with a compact boundary ∂Ω. We consider the following initial-boundary value problem (1) for the Navier-Stokes equations:
∇⋅v∂tv+(v⋅∇)v−νΔvvv(⋅,0)=0=−∇p=0=v0in Ω,in Ω,on ∂Ω,in Ω.
Of course, there is no boundary condition if Ω=Rm.
"In a recent paper [J. Math. Fluid Mech. 2 (2000), no. 1, 16--98] we investigated the strong solvability of (1) for initial data v0 belonging to certain spaces of distributions (modulo gradients). In this note we explain some of our main results in a very particular and simple setting. As usual, we concentrate on the velocity field v since the pressure field p is determined up to a constant by v.

Throughout this note m≥3 and either Ω=Rm, or Ω is a half-space of Rm, or Ω is a smooth domain in Rm with a compact boundary ∂Ω. We consider the following initial-boundary value problem (1) for the Navier-Stokes equations:
∇⋅v∂tv+(v⋅∇)v−νΔvvv(⋅,0)=0=−∇p=0=v0in Ω,in Ω,on ∂Ω,in Ω.
Of course, there is no boundary condition if Ω=Rm.
"In a recent paper [J. Math. Fluid Mech. 2 (2000), no. 1, 16--98] we investigated the strong solvability of (1) for initial data v0 belonging to certain spaces of distributions (modulo gradients). In this note we explain some of our main results in a very particular and simple setting. As usual, we concentrate on the velocity field v since the pressure field p is determined up to a constant by v.

Downloads

26 downloads since deposited on 29 Nov 2010
5 downloads since 12 months
Detailed statistics

Additional indexing

Other titles:International Conference on Differential and Functional Differential Equations (Moscow, 1999)
Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:maximal strong solution; Leray-Hopf weak solutions; exterior forces
Language:English
Date:2001
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Ariel University Center of Samaria
ISSN:0793-1786
Additional Information: © 2001 Ariel University Center of Samaria - All Rights Reserved.
Official URL:http://www.hit.ac.il/staff/benzionS/FDE.html
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1949984
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1060.35102
Permanent URL: https://doi.org/10.5167/uzh-21987

Download

[img]
Preview
Filetype: PDF
Size: 177kB

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations