Boundary Value Problem for Stationary Stokes Equations with Impermeability Boundary Condition
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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.
KeywordsWeak Solution Poisson Equation Neumann Problem Equivalent Norm Unique Weak Solution
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