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Existence results for third order nonlinear boundary value problems arising in nano boundary layer fluid flows over stretching surfaces. (English) Zbl 1231.35155
Summary: Solutions for a class of degenerate, nonlinear, nonlocal boundary value problems, arising in nano boundary layer fluid flows over a stretching surface, are obtained. Viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are considered. Using the Schauder fixed point theorem, existence and uniqueness results are established. The effects of the slip parameter $k$ and the suction parameter a on the fluid velocity and on the tangential stress are investigated and discussed (through numerical results). We find that for fluid flows at nanoscales, the shear stress at the wall decreases (in an absolute sense) with an increase in the slip parameter $k$.
##### MSC:
 35Q30 Stokes and Navier-Stokes equations 76D10 Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids) 35A01 Existence problems for PDE: global existence, local existence, non-existence 35A02 Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness