# American Institute of Mathematical Sciences

2011, 2011(Special): 135-144. doi: 10.3934/proc.2011.2011.135

## Mixed initial-boundary value problem for the three-dimensional Navier-Stokes equations in polyhedral domains

 1 Department of Mathematics, Centre for Integrated Design of Advanced Structures, Czech Technical University in Prague, Faculty of Civil Engineering, Thákurova 7, 166 29 Prague 6, Czech Republic

Received  July 2010 Revised  January 2011 Published  October 2011

We study a mixed initial{boundary value problem for the Navier{ Stokes equations, where the Dirichlet, Neumann and slip boundary conditions are prescribed on the faces of a three-dimensional polyhedral domain. We prove the existence, uniqueness and smoothness of the solution on a time interval (0, $T$*), where 0 $< T$* $<= T$.
Citation: Michal Beneš. Mixed initial-boundary value problem for the three-dimensional Navier-Stokes equations in polyhedral domains. Conference Publications, 2011, 2011 (Special) : 135-144. doi: 10.3934/proc.2011.2011.135
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