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http://dx.doi.org/10.4134/JKMS.2006.43.4.733

EXISTENCE OF QUASI-STATIONARY STOKES FLOW IN A DIHEDRAL DOMAIN  

Jin, Bum-Ja (Division of Mathematics College of Science Mokpo National University)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.4, 2006 , pp. 733-763 More about this Journal
Abstract
We study quasi-stationary Stokes flow in a dihedral domain arising from a study of a free boundary problem of viscous fluid in a container. We construct an exact solution of quasi-stationary Stokes equations and derive its estimates with norm in a weighted Sobolev spaces.
Keywords
dihedral domain; quasi-stationary; Stokes; existence; mixed boundary conditions;
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1 M. Abramowitz and I. A. Stegun, Handbook of Mathematical functions with for- mulas, graphs, and Mathematical tables, Dover, New York, 1966
2 M. Gunther and G. Prokert, Existence results for the quasistationary motion of a free capillary liquid drop, Z. Anal. Anwendungen 16 (1997), no. 2, 311-348   DOI
3 V. A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskov. Mat. Obs c . 16 (1967), 209-292
4 V. V. Pukhnachev and V. A. Solonnikov, On the problem of dynamic contact angle, J. Appl. Math. Mech. 46 (1982), no. 6, 771-779 (1983)   DOI   ScienceOn
5 V. A. Solonnikov, Solvability of the problem of the plane motion of a heavy viscous incompressible capillary fluid that partially fills a certain vessel, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 1, 203-236, 239
6 V. A. Solonnikov, Solvability of two stationary free boundary problems for the Navier- Stokes equations, Boll.Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (1998), no. 2, 283-342
7 V. A. Solonnikov, Solvability of two-dimensional free boundary problem for the Navier- Stokes equations for limiting values of contact angle, Recent developments in partial differential equations, 163-210, Quad. Mat, 2. Arance, Rome, (1998)
8 V. A. Solonnikov, On the Stokes equations in domains with nonsmooth boundaries and on viscous incompressible flow with a free surface, in Nonlinear Partial Differential Equations and their Applications, Colle de France Seminars, Vol. III, K. Brezis and J. L. Lions (editors), Research Notes in Mathematics, 70, Pitman, 340-423 (1982)
9 V. A. Solonnikov, Some free boundary problem for the Navier-Stokes equations with moving contact points and lines, Partial differential equations, 329-350, Math. Res., 82, Akademie-Verlag, Berlin (1994)
10 V. A. Solonnikov, On some free boundary problems for the Navier-stokes equations with moving contact points and lines, Math. Ann. 302 (1995), no. 4, 743-772   DOI
11 A. I. Markusevi, Theory of analytic function, Vol. 2, 2nd ed. 'Nauka', Moscow 1968, English transl. of 1st ed. Theorey of functions of a complex variables, Prentile-Hall, Englewood, Cliffs, N.J. 1965, 1967
12 V. V. Pukhnachev and V. A. Solonnikov, On the problem of dynamic contact angle, translated from Prikl. Mat. Mekh. 46 (1982), no. 6, 961-971. (Russian)
13 L. Stupelis, Navier-Stokes equations in irregular domains, Mathematics and its applications, Kluwer Academic Publishers Group, Dordrecht, 1995
14 J. Socolowsky, The solvability of a free boundary problem for the stationary Navier-Stokes equations with a dynamic contact line, Nonlinear Anal. 21 (1993), no. 10, 763-784   DOI   ScienceOn
15 J. Socolowsky, On a free boundary problem for the stationary Navier-Stokes equations with a dynamic contact line, The Navier-Stokes equations II-theory and numerical methods. Proceedings, Oberwolfach (1991). J. Heywood, K.Masuda, R.Rautman, V.Solonnikov (editors). Lecture Notes in Math. 1530, 17-29 (1992)
16 V. A. Solonnikov, Free boundary problems for the Navier-Stokes equations with moving contact point, Free boundary problems : theory and applications (1993), 203- 214, Pitman Res. Notes Math. Ser. 323, Longman Sci. Tech., Harlow, 1995
17 V. A. Solonnikov, On the justification of the quasistationary approximation in the problem of motion of viscous capillary drop, Interfaces Free Bbound. 1 (1999), no. 2, 125-173
18 V. A. Solonnikov and E. V. Frolova, On a problem with the third boundary con- dition for the Laplace equation in a plane angle, and its applications to parabolic problems, Leningrad Math. J. 2 (1991), no. 4, 891-916
19 D. H. Sattinger, On the free surface of a viscous fluid motion, Proc. Roy. Soc. London Ser. A 349 (1976), no. 1657, 183-204