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JOURNALS // Zapiski Nauchnykh Seminarov POMI

Zap. Nauchn. Sem. LOMI, 1977, Volume 69, Pages 200–218 (Mi znsl1992)

The solvability of the second initial boundary-value problem for the linear, time-dependent system of Navier–Stokes equations
V. A. Solonnikov

This publication is cited in the following articles:
  1. Giusy Mazzone, “Local well-posedness of the equations governing the motion of a fluid-filled elastic solid”, Res Math Sci, 12:4 (2025)  crossref
  2. Shibata Y. Zajaczkowski W.M., “On Local Solutions to a Free Boundary Problem For Incompressible Viscous Magnetohydrodynamics in the l-P-Approach”, Diss. Math., 2021  crossref  isi
  3. Vsevolod Alexeevich Solonnikov, Irina Vladimirovna Denisova, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, 1  crossref
  4. Vsevolod Alexeevich Solonnikov, Irina Vladimirovna Denisova, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, 1135  crossref
  5. Vsevolod Alexeevich Solonnikov, Irina Vlad. Denisova, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2017, 1  crossref
  6. Zajaczkowski W.M., “Nonstationary Stokes System in Anisotropic Sobolev Spaces”, Math. Meth. Appl. Sci., 38:12 (2015), 2466–2478  crossref  isi
  7. V. A. Solonnikov, “L p -Theory of the Problem of Motion of Two Incompressible Capillary Fluids in a Container”, J Math Sci, 198:6 (2014), 761  crossref
  8. Matthias Köhne, Lp-Theory for Incompressible Newtonian Flows, 2013, 35  crossref
  9. Dieter Bothe, Matthias Köhne, Jan Prüss, “On a Class of Energy Preserving Boundary Conditions for Incompressible Newtonian Flows”, SIAM J. Math. Anal., 45:6 (2013), 3768  crossref
  10. V. A. Solonnikov, “$L_p$-estimates of solutions of a linear problem arising in magnetohydrodynamics”, St. Petersburg Math. J., 23:1 (2012), 161–177  mathnet  crossref  mathscinet  zmath  isi  elib
  11. Alexandre Caboussat, “Numerical simulation of two-phase free surface flows”, Arch. Comput. Meth. Engng., 12:2 (2005), 165  crossref
  12. V. A. Solonnikov, “On estimates of solutions of the non-stationary Stokes problem in anisotropic Sobolev spaces and on estimates for the resolvent of the Stokes operator”, Russian Math. Surveys, 58:2 (2003), 331–365  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  13. Solonnikov V.A., “Lectures on evolution free boundary problems: Classical solutions”, Mathematical Aspects of Evolving Interfaces, Lecture Notes in Mathematics, 1812, 2003, 123–175  crossref  zmath  isi
  14. Alexander Kozhevnikov, Olga Lepsky, “Power series solutions to basic stationary boundary value problems of elasticity”, Integr equ oper theory, 31:4 (1998), 449  crossref
  15. Naoto TANAKA, “Two-phase free boundary problem for viscous incompressible thermo-capillary convection”, Jpn. j. math, 21:1 (1995), 1  crossref
  16. G. Grubb, V. A. Solonnikov, “Reduction of the fundamental initial-boundary-value problems for Stokes equations to initial-boundary-value problems for parabolic systems of pseudodifferential equations”, J Math Sci, 49:5 (1990), 1140  crossref
  17. V. A. Solonnikov, “Unsteady motion of a finite mass of fluid, bounded by a free surface”, J Math Sci, 40:5 (1988), 672  crossref
  18. B. V. Bazalii, S. P. Degtyarev, “On classical solvability of the multidimensional Stefan problem for convective motion of a viscous incompressible fluid”, Math. USSR-Sb., 60:1 (1988), 1–17  mathnet  crossref  mathscinet  zmath
  19. V. A. Solonnikov, “On the transient motion of an isolated volume of viscous incompressible fluid”, Math. USSR-Izv., 31:2 (1988), 381–405  mathnet  crossref  mathscinet  zmath
  20. G. Allain, “Small-time existence for the Navier-Stokes equations with a free surface”, Appl Math Optim, 16:1 (1987), 37  crossref
  21. I. Sh. Mogilevskii, “On a boundary value problem for the time-dependent Stokes system with general boundary conditions”, Math. USSR-Izv., 28:1 (1987), 37–66  mathnet  crossref  mathscinet  zmath
  22. Geneviève Allain, “Un problème de Navier-Stokes avec surface libre et tension superficielle”, Annales de la Faculté des sciences de Toulouse : Mathématiques, 7:1 (1985), 29  crossref
  23. J. T. Beale, “Large-time regularity of viscous surface waves”, Arch. Rational Mech. Anal., 84:4 (1984), 307  crossref
  24. Michael Renardy, “Local existence theorems for the first and second initial-boundary value problems for a weakly non-newtonian fluid”, Arch. Rational Mech. Anal., 83:3 (1983), 229  crossref
  25. J. Thomas Beale, “The initial value problem for the navier‐stokes equations with a free surface”, Comm Pure Appl Math, 34:3 (1981), 359  crossref
  26. V. A. Solonnikov, “Solvability of a problem on the motion of a viscous incompressible fluid bounded by a free surface”, Math. USSR-Izv., 11:6 (1977), 1323–1358  mathnet  crossref  mathscinet  zmath


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