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Strong solutions of doubly nonlinear Navier-Stokes equations

Pages: 1052 - 1060, Issue Special, September 2011

 Abstract        Full Text (337.3K)              

Jochen Merker - Universität Rostock, Institut für Mathematik, Universitätsplatz 1, 18051 Rostock, Germany (email)

Abstract: In this article existence of weak and strong solutions to doubly nonlinear incompressible Navier-Stokes equations

$(\partialb(u))/(\partialt)+$div$(b(u)\times u) = $-$d\pi +$div$\(a(\nabla^(sym)u)) + f,$     div$(u)=0,$
is discussed, where $u$ models the velocity vector field of a homogeneous non-Newtonian fluid whose momentum $b(u)$ depends nonlinearly on $u$.

Keywords:  Navier-Stokes equations, doubly nonlinear evolution equations, strong solutions
Mathematics Subject Classification:  Primary: 35K55, 35Q30; Secondary: 76D05.

Received: July 2010;      Revised: July 2011;      Published: October 2011.