Abstract
We consider a boundary-value problem for the stationary flow of an incompressible second-grade fluid in a bounded domain. The boundary condition allows for no-slip, Navier type slip, and free slip on different parts of the boundary. We first establish the well-posedness of a linear auxiliary problem by means of a fixed-point argument in which the problem is decomposed into a Stokes-type problem and two transport equations. Then we use the method of successive approximations to prove the unique solvability of the nonlinear problem with a sufficiently small body force in Holder spaces. Bibliography: 17 titles.
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Dedicated to Professor Vsevolod A. Solonnikov on his seventieth birthday
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 210–228.
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Tani, A., Le Roux, C. Steady-State Solutions to the Equations of Motion of Second-Grade Fluids with General Navier Type Slip Boundary Conditions in Holder Spaces. J Math Sci 130, 4899–4909 (2005). https://doi.org/10.1007/s10958-005-0385-7
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DOI: https://doi.org/10.1007/s10958-005-0385-7