Asymptotic modelling of a piston with a completely wetted surface
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 34, Tome 306 (2003), pp. 53-70 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A quasi-stationary model is constructed for a lubricated piston by coupling a two-dimensional Reynolds equation with three-dimensional Navier–Stokes equations. This hybrid problem is shown to be well-posed in weighted Sobolev spaces with attached asymptotics.
@article{ZNSL_2003_306_a2,
     author = {J. H. Videman and S. A. Nazarov and A. Sequeira},
     title = {Asymptotic modelling of a~piston with a~completely wetted surface},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--70},
     year = {2003},
     volume = {306},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a2/}
}
TY  - JOUR
AU  - J. H. Videman
AU  - S. A. Nazarov
AU  - A. Sequeira
TI  - Asymptotic modelling of a piston with a completely wetted surface
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 53
EP  - 70
VL  - 306
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a2/
LA  - en
ID  - ZNSL_2003_306_a2
ER  - 
%0 Journal Article
%A J. H. Videman
%A S. A. Nazarov
%A A. Sequeira
%T Asymptotic modelling of a piston with a completely wetted surface
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 53-70
%V 306
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a2/
%G en
%F ZNSL_2003_306_a2
J. H. Videman; S. A. Nazarov; A. Sequeira. Asymptotic modelling of a piston with a completely wetted surface. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 34, Tome 306 (2003), pp. 53-70. http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a2/

[1] O. Reynolds, “On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments”, Philos. Trans. Roy. Soc., 177 (1886), 157–234 | DOI

[2] V. A. Solonnikov, “On the problem of a moving contact angle”, Nonlinear Analysis and Continuum Mechanics, eds. G. Buttazzo et al., Springer, 1998, 107–137 | MR

[3] D. Kröner, “Asymptotic expansions for a flow with a dynamic contact angle”, Navier Stokes Equations, Springer LNM, 1431, eds. J. G. Heywood et al., Springer, 1990, 49–59 | MR

[4] S. A. Nazarov, B. A. Plamenevskii, “Selfadjoint elliptic problems with radiation conditions on the edges of the boundary”, Algebra Analiz, 4 (1992), 196–225 | MR | Zbl

[5] S. A. Nazarov, “The Navier-Stokes problem in a two-dimensional domain with angular outlets to infinity”, Zap. Nauchn. Sem. St.-Petersburg Otdel. Mat. Inst. Steklov, 257, 1999, 207–227 | MR | Zbl

[6] S. A. Nazarov, “Junctions of singularly degenerating domains with different limit dimensions, 2”, Trudy Sem. Petrovskii, 20, 1997, 155–195 | MR | Zbl

[7] V. G. Maz'ya, A. S. Slutskij, “Asymptotic analysis of the Navier–Stokes system in a plane domain with thin channels”, Asymptot. Anal., 23 (2000), 59–89 | MR

[8] V. A. Solonnikov, “Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling the container”, Izv. Akad. Nauk SSSR (Ser. Mat.), 43 (1979), 203–236 | MR | Zbl

[9] S. A. Nazarov, K. Pileckas, “On steady Stokes and Navier–Stokes problems with zero velocity at infinity in a three-dimensional exterior domain”, J. Math. Kyoto Univ., 40 (2000), 475–492 | MR | Zbl

[10] S. A. Nazarov, A. Sequeira, J. H. Videman, “Steady flows of Jeffrey-Hamel type from the half-plane into an infinite channel. 1: Linearization on an antisymmetric solution”, J. Math. Pures Appl., 80 (2001), 1069–1098 | DOI | MR | Zbl

[11] B. W. Schulze, Boundary Value Problems and Singular Pseudo-Differential Operators, John Wiley Sons, Chichester, 1998 | MR | Zbl

[12] S. A. Nazarov, “Asymptotic solution of the Navier-Stokes problem on the flow of a thin layer of fluid”, Sibirsk. Mat. Zh., 31 (1990), 131–144 | MR | Zbl

[13] S. A. Nazarov, K. I. Pileckas, “Reynolds flow of a fluid in a thin three-dimensional channel”, Litovsk. Mat. Sb., 30 (1990), 772–783 | MR | Zbl

[14] S. A. Nazarov, J. H. Videman, “Reynolds type equation for a thin flow under intensive transverse percolation”, Math. Nachr. (to appear) | MR

[15] O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Springer, 1985 | MR

[16] A. Z. Szeri, Fluid Film Lubrication: Theory and Design, Cambridge University Press, 1998 | Zbl