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

Pages: 135 - 144, Issue Special, September 2011

 Abstract        Full Text (377.0K)              

Michal BeneŇ° - Department of Mathematics, Centre for Integrated Design of Advanced Structures, Czech Technical University in Prague, Faculty of Civil Engineering, Th√°kurova 7, 166 29 Prague 6, Czech Republic (email)

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 $< T$* $<= T$.

Keywords:  Navier-Stokes equations, regularity of generalized solutions, mixed boundary conditions
Mathematics Subject Classification:  Primary: 35Q30; Secondary: 35D10

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