On free boundary problems with moving contact points for the stationary two-dimensional Navier-Stokes equations
- 61 Downloads
Solvability of the problem of slow drying of a plane capillary in the classical setting (i. e., with the adherence condition on a rigid wall) is established. The proof is based on a detailed study of the asymptotics of the solution near a point of contact of the free boundary with a moving wall, including estimates of the coefficients in well known asymptotic formulas. It is shown that the only value of the contact angle admitting a solution of the problem with finite energy dissipation equals π. Bibliography: 18 titles.
KeywordsContact Angle Energy Dissipation Contact Point Free Boundary Boundary Problem
Unable to display preview. Download preview PDF.
- 1.V. V. Pukhnachov and V. A. Solonnikov, “On the problem of dynamic contact angle,”Prikl. Mat. Mekh.,46, 961–971 (1982).Google Scholar
- 2.V. A. Solonnikov, “On the solvability of some two-dimensional quasistationary free boundary problems for the Navier-Stokes equations with a moving contact point,”Zap. Nauchn. Semin. POMI, 119–126 (1993).Google Scholar
- 3.V. A. Solonnikov, “On the problem of a moving contact angle,” University of Paderborn, preprint (1993).Google Scholar
- 4.V. A. Solonnikov, “On some free boundary problems for the Navier-Stokes equations with moving contact points and lines” (to appear).Google Scholar
- 10.K. Bayokki and V. V. Pukhachov, “Problems with one-sided restrictions for the Navier-Stokes equations and the dynamic boundary angle problem,”Prikl. Mekh. Tekch. Fiz.,2, 27–40 (1990).Google Scholar
- 11.J. Socolowsky, “On a free boundary problem for the stationary Navier-Stokes equations with a dynamic contact line,”Proceedings Oberwolfach 1991. Lect. Notes in Math., Springer-Verlag.Google Scholar
- 12.L. K. Antanowskii, “Boundary integral equations for contact problems of plane quasi-steady viscous flow,”Europ. J. Appl. Math.,4, 175–187 (1993).Google Scholar
- 15.V. V. Pukhnachov, “Plane stationary free boundary problem for the Navier-Stokes equations,”Prikl. Mekh. Tekh. Fiz.,3, 91–102 (1972).Google Scholar
- 18.V. A. Solonnikov, “On the Stokes equations in domains with non-smooth boundaries and on viscous flow with a free surface,”Nonlinear part. diff. equations and their applications. College de France Seminars,3,Research Notes Math., No. 74, 340–423 (1981).Google Scholar