Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21987
Amann, H (2001). Remarks on the strong solvability of the Navier-Stokes equations. Functional Differential Equations, 8(1-2):3-9.
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.
|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|
|Uncontrolled Keywords:||maximal strong solution; Leray-Hopf weak solutions; exterior forces|
|Deposited On:||29 Nov 2010 17:27|
|Last Modified:||17 Dec 2012 07:29|
|Publisher:||Ariel University Center of Samaria|
|Additional Information:||© 2001 Ariel University Center of Samaria - All Rights Reserved.|
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