Abstract
This chapter is a continuation of paper [1] devoted to the investigation of the asymptotics of a solution of the two-dimensional Navier—Stokes equations in the neighborhood of the point of a contact of the free boundary with a uniformly moving rigid wall. The contact angle is supposed to equal π. In [1] it was shown in particular that in the neighborhood of the contact point x = 0 the free surface is given by the equation of the type \(h\left( {{x_1}} \right) = cx_1^{2 - k} + o\left( {x_1^{2 - k}} \right)\), x 1 ∈ (0, d), where c and κ are certain numbers depending on the velocity of the bottom x 2 = 0. In the present chapter, we estimate the constant c and obtain the information on its sign. This information can be used for the proof of the solvability of free boundary problems where such a contact occurs. In this chapter, we restrict ourselves to the simplest problem of filling an infinite plane capillary, without taking into consideration the force of gravity, and to the piston problem.
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Solonnikov, V.A. (1998). On the Problem of a Moving Contact Angle. In: Buttazzo, G., Galdi, G.P., Lanconelli, E., Pucci, P. (eds) Nonlinear Analysis and Continuum Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2196-8_10
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DOI: https://doi.org/10.1007/978-1-4612-2196-8_10
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