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2011, 2011(Special): 1052-1060. doi: 10.3934/proc.2011.2011.1052

Strong solutions of doubly nonlinear Navier-Stokes equations

Jochen Merker 1,

1. 

Universität Rostock, Institut für Mathematik, Universitätsplatz 1, 18051 Rostock

Received  July 2010 Revised  July 2011 Published  October 2011

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, strong solutions, doubly nonlinear evolution equations.
Mathematics Subject Classification: Primary: 35K55, 35Q30; Secondary: 76D0.
Citation: Jochen Merker. Strong solutions of doubly nonlinear Navier-Stokes equations. Conference Publications, 2011, 2011 (Special) : 1052-1060. doi: 10.3934/proc.2011.2011.1052
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