Leray’s problem on the stationary Navier–Stokes equations with inhomogeneous boundary data
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Consider the stationary Navier–Stokes equations in a bounded domain whose boundary consists of multi-connected components. We investigate the solvability under the general flux condition which implies that the total sum of the flux of the given data on each component of the boundary is equal to zero. Based on our Helmholtz–Weyl decomposition, we prove existence of solutions if the harmonic part of the solenoidal extension of the given boundary data is sufficiently small in L 3 compared with the viscosity constant.
KeywordsWeak Solution Stokes Equation Boundary Data Sobolev Inequality Compact Riemannian Manifold
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