Journal of Mathematical Sciences

, Volume 207, Issue 2, pp 195–205 | Cite as

Boundary Value Problem for Stationary Stokes Equations with Impermeability Boundary Condition

  • Yu. A. Dubinskii

We propose two approaches to the study of the boundary value problem for the stationary Stokes equations with impermeability boundary condition. The first approach is classical and is based on a Friedrichs type inequality and a variant of the de Rham theorem. The second approach is based on solving the boundary value problem with the impermeability condition for the system of Poisson equations and decomposition of a Sobolev space into the sum of solenoidal and potential subspaces. We also study the gradient-divergence boundary value problem with impermeability boundary condition and establish the corresponding Ladyzhenskaya–Babushka–Brezzi inequality.


Weak Solution Poisson Equation Neumann Problem Equivalent Norm Unique Weak Solution 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.National Research University “Moscow Power Engineering Institute”MoscowRussia

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