Geodesic
Steady-state solutions to the equations of motion of second-grade fluids with general Navier-type slip boundary conditions in H\"older spaces
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 34, Tome 306 (2003), pp. 210-228

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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 it is decomposed into a Stokes-type problem and two transport equations. Then we use the method of successive approximations to prove the unique solvability in Hölder spaces of the nonlinear problem with a sufficiently small body force. 
@article{ZNSL_2003_306_a10,
     author = {A. Tani and C. Le Roux},
     title = {Steady-state solutions to the equations of motion of second-grade fluids with general {Navier-type} slip boundary conditions in {H\"older} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {210--228},
     publisher = {mathdoc},
     volume = {306},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a10/}
}
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A. Tani; C. Le Roux. Steady-state solutions to the equations of motion of second-grade fluids with general Navier-type slip boundary conditions in H\"older spaces. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 34, Tome 306 (2003), pp. 210-228. http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a10/