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.
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.
References
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.
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.
O. V. Besov—V. P. Il’in—S. M. Nicol’skii,Integral representation of functions and imbedding theorems, Nauka, Moscow (1975).
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.
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.
K. K. Golovkin—O. 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.
G. Grubb,Functional calculus of pseudodoiierential boundary problems, Birkhäuser, 1996.
G. Grubb,Nonhomogeneous time-dependent Navier-Stokes problems in L p Sobolev spaces, Diff. Int. Equat.,8 (1995), pp. 1013–1046.
G. Grubb—V. 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.
S. N. Kruzhkov—A. Castro—M. 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.
O. A. Ladyzhenskaya,On nonlinear problems of continuum mechanics, Proc. Int. Congress Math. (Moscow, 1966), Nauka, Moskow, 1968, 560–573.
O. A. Ladyzhenskaya,Mathematical problems of viscous incompressible flow, Gordon and Breach, 1969.
O. A. Ladyzhenskaya—V. A. Solonnikov—N. N. Uraltseva,Linear and quasilinear equations of parabolic type, Nauka, Moskow, 1967.
J. Málek—J. Nečas—M. Rokyta—M. Růzhička,Weak and measure-valued solutions to evolution partial differential equations, Chapman and Hall, 1996.
P. Maremonti—V. 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.
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.
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.
G. A. Seregin,Interior regularity for solutions to the modified Navier-Stokes equations, J. math. fluid mech.,1 (1999), pp. 235–281.
V. A. Solonnikov,Estimates of solutions of nonstationary linearized Navier-Stokes equations, Trudy Math. Inst. Steklov,70 (1964), pp. 213–317.
V. A. Solonnikov,Estimates of solutions of nonstationary Navier-Stokes equations, Zap. Nauchn. semin. L.O.M.I.,38 (1973), pp. 153–231.
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.
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Dedicated to the memory of Professor S. N. Kruzhkov
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Solonnikov, V.A. On the solvability of generalized Stokes equations in the spaces of periodic functions. Ann. Univ. Ferrara 46, 219–249 (2000). https://doi.org/10.1007/BF02837300
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DOI: https://doi.org/10.1007/BF02837300