The asymptotic form of the Navier-Stokes equations along the contact line of two surfaces. (English) Zbl 1090.76518
Summary: We study the motion of a viscous incompressible fluid in a neighbourhood of a contact line of two surfaces. Our analysis shows that in this region the three-dimensional motion can be decomposed into a two-dimensional Stokes flow in plane normal to the contact line and a Couette flow along this curve.
A similar analysis for the three-dimensional electrostatic problem was performed by O. K. Aksentyan [Prikl. Mat. Mekh. 31, 178–186 (1967; Zbl 0153.28004)] (see also [V. Z. Parton and P. I. Perlin, Mathematical methods of the theory of elasticity. Mir Publishers, Moscow (1984; Zbl 0626.73001)]).
A similar analysis for the three-dimensional electrostatic problem was performed by O. K. Aksentyan [Prikl. Mat. Mekh. 31, 178–186 (1967; Zbl 0153.28004)] (see also [V. Z. Parton and P. I. Perlin, Mathematical methods of the theory of elasticity. Mir Publishers, Moscow (1984; Zbl 0626.73001)]).
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
| 35Q30 | Navier-Stokes equations |
