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Note on the kinematics of plane viscous motion

1950
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Quarterly of Applied Mathematics
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an interesting result, which may be stated as follows: Let R be a finite plane region with boundary B. Then the equation Aip = F possesses a solution for which both and dip/dn vanish on B if and only if F satisfies U being an arbitrary harmonic function. In other words, for the existence of a solution with this double boundary condition, it is necessary and sufficient that the function F be orthogonal to the linear space of harmonic functions. The hydrodynamical interpretation of Hamel's

doi:10.1090/qam/36109
fatcat:66khmi7lzbhkhgeks3swzj3swm