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

Michal Beneš

doi:10.3934/proc.2011.2011.135

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2011, Volume 2011: 135-144. Doi: 10.3934/proc.2011.2011.135 open access

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

Michal Beneš^1,

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

Received: July 2010

Revised: January 2011

Published: August 2017

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Abstract

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 $< T$* $<= T$.

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 35D10.

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

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