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Annali dell’Università di Ferrara

, Volume 46, Issue 1, pp 219–249 | Cite as

On the solvability of generalized Stokes equations in the spaces of periodic functions

  • V. A. Solonnikov
Article
  • 45 Downloads

Abstract

The paper is concerned with the solvability theory of the generalized Stokes equations arising in the study of the motion of non-newtonian fluids.

Keywords

Cauchy Problem Stokes System Finite Norm Coercive Estimate Degenerate Parabolic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sunto

Il lavoro si occupa della teoria dell’esistenza di soluzioni per le equazioni generalizzate di Stokes motivate dallo studio del moto di fluidi non newtoniani.

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References

  1. [1]
    M. A. Abdrakhmanov,A priori L 2 -estimates for solutions of an initial-boundary value problem for a system of two equations of general type that has a mixed parabolic-elliptic structure, Diff. Uravn.,26 (1990), pp. 2163–2165.MATHMathSciNetGoogle Scholar
  2. [2]
    M. A. Abdrakhmanov,L p -estimates for solutions of general boundary value problems for an equation with mixed parabolic-elliptic structure, Zap. Nauchn. Semin. P.O.M.I.,197 (1992), pp. 4–27.Google Scholar
  3. [3]
    O. V. BesovV. P. Il’inS. M. Nicol’skii,Integral representation of functions and imbedding theorems, Nauka, Moscow (1975).Google Scholar
  4. [4]
    M. E. Bogovskii,Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Sov. Math. Doklady,20 (1979), pp. 1094–1098.Google Scholar
  5. [5]
    K. K. Golovkin,Certain conditions for the smoothness of a function of several variables and estimates of convolution operators, Doklady Acad. Sci. USSR,139 (1961), pp. 524–527.MathSciNetGoogle Scholar
  6. [6]
    K. K. GolovkinO. A. Ladyzhenskaya,On solutions of the nonstationary boundary value problem for the Navier-Stokes equations, Trudy V. A. Steklov Math. Inst.,59 (1960), pp. 100–114.MATHGoogle Scholar
  7. [7]
    G. Grubb,Functional calculus of pseudodoiierential boundary problems, Birkhäuser, 1996.Google Scholar
  8. [8]
    G. Grubb,Nonhomogeneous time-dependent Navier-Stokes problems in L p Sobolev spaces, Diff. Int. Equat.,8 (1995), pp. 1013–1046.MATHMathSciNetGoogle Scholar
  9. [9]
    G. GrubbV. A. Solonnikov,Reduction of basic initial-value problems for the Stokes equations to initial-boundary value problems for systems of pseudodifferential equations, Zap. Nauchn. Semin. L.O.M.I.,163 (1987), pp. 37–48.Google Scholar
  10. [10]
    S. N. KruzhkovA. CastroM. Lopes,Mayoraciones de Schauder y teorema de existencia de las soluciones del problema de Cauchy para equaciones parabolicas lineales y no lineales (1), Ciencias Matemáticas,1 (1980), pp. 57–76; (II), Ciencias Matemáticas,3 (1982), pp. 37–56.Google Scholar
  11. [11]
    O. A. Ladyzhenskaya,On nonlinear problems of continuum mechanics, Proc. Int. Congress Math. (Moscow, 1966), Nauka, Moskow, 1968, 560–573.Google Scholar
  12. [12]
    O. A. Ladyzhenskaya,Mathematical problems of viscous incompressible flow, Gordon and Breach, 1969.Google Scholar
  13. [13]
    O. A. LadyzhenskayaV. A. SolonnikovN. N. Uraltseva,Linear and quasilinear equations of parabolic type, Nauka, Moskow, 1967.Google Scholar
  14. [14]
    J. Málek—J. Nečas—M. Rokyta—M. Růzhička,Weak and measure-valued solutions to evolution partial differential equations, Chapman and Hall, 1996.Google Scholar
  15. [15]
    P. MaremontiV. A. Solonnikov,Estimates of solutions of nonstationary Stokes problem in anisotropic S. L. Sobolev spaces with a mixed norm, Zap. Nauchn. Semin. L.O.M.I.,222 (1995), pp. 88–125.Google Scholar
  16. [16]
    I. Sh. Mogilevskii,Estimates for the solutions of general initial-boundary value problem for a linear nonstationary system of Navier-Stokes equations in a bounded domain, Trudy Math. Inst. Steklov,159 (1983), pp. 61–94.MathSciNetGoogle Scholar
  17. [17]
    I. Sh. Mogilevskii,A boundary value problem for a nonstationary Stokes system with general boundary conditions, Izv. Acad Nauk SSSR, ser. mat.,50 (1986), pp. 37–66.MathSciNetGoogle Scholar
  18. [18]
    G. A. Seregin,Interior regularity for solutions to the modified Navier-Stokes equations, J. math. fluid mech.,1 (1999), pp. 235–281.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    V. A. Solonnikov,Estimates of solutions of nonstationary linearized Navier-Stokes equations, Trudy Math. Inst. Steklov,70 (1964), pp. 213–317.MATHMathSciNetGoogle Scholar
  20. [20]
    V. A. Solonnikov,Estimates of solutions of nonstationary Navier-Stokes equations, Zap. Nauchn. semin. L.O.M.I.,38 (1973), pp. 153–231.MathSciNetGoogle Scholar
  21. [21]
    V. A. Solonnikov,Estimates of solutions of the second initial-boundary value problem for the Stokes system in the space of functions with Hölder continuous derivatives with respect to spatial variables, Zap. Nauchn. Semin. P.O.M.I.,259 (1999), pp. 254–279.Google Scholar

Copyright information

© Università degli Studi di Ferrara 2000

Authors and Affiliations

  • V. A. Solonnikov
    • 1
  1. 1.Dipartimento di MatematicaUniversità di FerraraFerrara

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