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On some free boundary problems for the Navier-Stokes equations with moving contact points and lines

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References

  1. C. Huh, L.E. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interf. Sci.,35 (1971), 85–101

    Google Scholar 

  2. E.B. Dussan, S.H. Davis, On the motion of the fluid-fluid interface along a solid surface. J. Fluid Mech.,65 (1974), 71–95

    Google Scholar 

  3. E.B. Dussan, The moving contact line: the slip boundary condition. J. Fluid Mech.,77 (1976), 665–684

    Google Scholar 

  4. L.M. Hocking, A moving fluid interface, II. The removal of the force singularity by a slip flow. J. Fluid Mech.,79 (1977), 209–229

    Google Scholar 

  5. V.A. Pukhnachov, V.A. Solonnikov, On the problem of dynamic contact angle. J. Appl. Math. and Mech.,46 (1982), 771–779

    Google Scholar 

  6. D. Kröner, The flow of a fluid with a free boundary and dynamic contact angle. The Navier-Stokes equations: theory and numerical methods. Proceedings, Oberwolfach 1988. J. Heywood, K. Masuda, R. Rautmann, V. Solonnikov (editors). Lecture Notes in Math.,1431 (1990), 49–59

  7. Jü. 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. Rautmann, V. Solonnikov (editors). Lecture Notes in Math.,1530 (1992), 17–29

  8. C. Baiocchi, V.V. Pukhnachov, Unilateral problems for the Navier-Stokes equations and problem of dynamical contact angle. J. Appl. Mech. and Techn. Physics, Nr 2 (1990), 27–42

    Google Scholar 

  9. V.A. Solonnikov, On the problem of a moving contact angle. Univ. of Paderborn, Preprint, 1993

  10. V.A. Solonnikov, On free boundary problems with moving contact points for two-dimensional stationary Navier-Stokes equations. Zap. Nauchn. Semin. POMI,213 (1994), 179–205

    Google Scholar 

  11. V.A. Solonnikov, On the solvability of some two-dimensional quasistationary free boundary problems for the Navier-Stokes equations with moving contact points. Zap. Nauchn. Semin. POMI206 (1993), 119–126

    Google Scholar 

  12. A. Friedman, J.L. Velázquez, The analysis of coating flows near the contact line. IMA Preprint, 1993.

  13. A. Friedman, J.L. Velázquez, The analysis of coating flows in a strip. IMA Preprint,1135 (1993)

  14. L.K. Antanovskii, Boundary integral equations for contact problems of plane viscous flow. Eur. J. Appl. Math.,4 (1993), 175–187

    Google Scholar 

  15. V.A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical and angular points. Trudy Moscow Math. Obšč.,16 (1967), 207–292

    Google Scholar 

  16. V.G. Maz'ya, B.A. Plamenevskii, Estimates inL p and in Hölder spaces and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems with singular points at the boundary. Math. Nachrichten,81, (1978), 25–82

    Google Scholar 

  17. V.G. Maz'ya, B.A. Plamenevskii, On the coefficents in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Math. Nachrichten,76 (1977), 29–60

    Google Scholar 

  18. V.A. Solonnikov, V.E. Šcadilov, On the boundary value problem for stationary system of Navier-Stokes equations. Trudy Inst. Math. Steklov.,125 (1973), 196–210

    Google Scholar 

  19. O.A. Ladyzhenskaya, V.A. Solonnikov, Determination of solutions of boundary value problems for steady-state Stokes and Navier-Stokes equations having an infinite Dirichlet integral. Zap. Nauchn. Semin. LOMI,96 (1980), 117–160

    Google Scholar 

  20. V.A. Solonnikov, Stokes and Navier-Stokes equations in domains with non-compact boundaries. Nonlinear partial differential equations and their applications. College de France seminar, vol. IV. H. Brezis and J.-L. Lions (editors). Research notes in mathematics,84 (1983), 240–349

  21. V.A. Solonnikov, Solvability of three-dimensional free boundary for stationary system of Navier-Stokes equations. Zap. Nauchn. Semin. LOMI,84 (1980), 252–285

    Google Scholar 

  22. V.A. Solonnikov, Solvability of a three-dimensional boundary value problem with a free boundary for the stationary Navier-Stokes system. Banach Center Publ.,10 (1983), 361–403

    Google Scholar 

  23. V.G. Maz'ya, B.A. Plamenevskii, L.I. Stupelis, Three-dimensional problem of the steady-state motion of fluid with a free surface. Diff. equations and their application,23 (1979), 6–153

    Google Scholar 

  24. Jü. Socolowsky, The solvability of a free boundary problem for the stationary Navier-Stokes equations with a dynamic contact angle. Nonlinear Analysis. Theory, methods and applications,21 (1993), 763–784

    Google Scholar 

  25. K. Pileckas, Solvability of problem on the motion on the plane of viscous incompressible fluid with noncompact free surface. Diff. equations and their applications,30 (1981), 57–96

    Google Scholar 

  26. K. Pileckas, M. Specovius-Neugebauer, Solvability of a non-compact free boundary problem for the stationary Navier-Stokes system, I, Lit. Math. Sbornik,29 (1989), 532–547, II, Lit. Math. Sbornik, 29 (1989), 773–784

    Google Scholar 

  27. L.D. Landau, E.M. Lifschitz, Mechanics of continuum media, Oxford 1959

  28. Jü. Socolowsky, Elementary investigation of the equation for a free surface. Techn. Mechanik,12 (1991), 257–259

    Google Scholar 

  29. V.A. Solonnikov, On the Stokes equations in domains with non-smooth boundaries and on viscous flow with a free surface. Nonlinear partial differential equations and their applications. College de France seminars, vol. III. H. Brezis and J.-L. Lions (editors). Research notes in mathematics,70 (1981), 340–423

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  1. St. Petersburg Branch of V.A. Steklov Mathematical Institute of the Russian Academy of Sciences, Fontanka 27, 191011, St. Petersburg, Russia

    V. A. Solonnikov

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Solonnikov, V.A. On some free boundary problems for the Navier-Stokes equations with moving contact points and lines. Math. Ann. 302, 743–772 (1995). https://doi.org/10.1007/BF01444515

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