# American Institute of Mathematical Sciences

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

## Strong solutions of doubly nonlinear Navier-Stokes equations

 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 $u$.
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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