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Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces. (English) Zbl 1121.35098
The authors investigate the analytic regularity analytic data. They introduce weighted Sobolev spaces related to Kondrat’ev’s weighted spaces. The authors establish a shift theorem near the corners.

MSC:
35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35A20 Analyticity in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
76D07 Stokes and related (Oseen, etc.) flows
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[1] Agranovich, M.S.; Vishik, M.K., Elliptic problems with a parameter and parabolic problems of general type, Uspekhi mat. nauk., 19, 3, 626-727, (1959), (Russian Math. Surveys 19(3) (1964) 53-157)
[2] Babuška, I.; Guo, B.Q., Regularity of the solution of elliptic problems with piecewise analytic data. part 1. boundary value problems for linear elliptic equation of second order, SIAM J. math. anal., 19, 172-203, (1988) · Zbl 0647.35021
[3] Babuška, I.; Guo, B.Q., The h-p version of the finite element method with curved boundary, SIAM J. numer. anal., 24, 837-861, (1988) · Zbl 0655.65124
[4] Babuška, I.; Guo, B.Q., Regularity of the solution of elliptic problems with piecewise analytic data. part 2. the trace spaces and application to boundary value problems with non-homogeneous conditions, SIAM J. math. anal., 20, 763-781, (1989) · Zbl 0706.35028
[5] Babuška, I.; Suri, M., The h-p version of the finite element method with quasi-uniform meshes, RAIRO, math. mod. numer. anal., 21, 199-238, (1987) · Zbl 0623.65113
[6] Babuška, I.; Suri, M., The optimal convergence rate of the p-version of the finite element method, SIAM J. numer anal., 24, 750-776, (1991) · Zbl 0637.65103
[7] I. Babuška, M. Szabó, N. Katz, The p-version of the finite element method, SIAM J. Numer Anal. (1981) 515-545.
[8] Bolley, P.; Dauge, M.; Camus, J., Regularité Gevrey pour le problème de Dirichlet dans des domaines à singularités coniques, Comm. partial differential equations, 10, 4, 391-431, (1985) · Zbl 0573.35024
[9] Brezzi, F., On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO anal. numer., 8, 129-151, (1994) · Zbl 0338.90047
[10] Dauge, M., Stationary Stokes and navier – stokes systems on two- or three-dimensional domains with corners I: linearized equations, SIAM J. math. anal., 20, 74-97, (1989) · Zbl 0681.35071
[11] Galdi, G., An introduction to the mathematical theory of the navier – stokes equations, (1994), Springer Heidelberg
[12] Girault, V.; Raviart, P.A., Finite element methods for navier – stokes equations, (1986), Springer Berlin · Zbl 0396.65070
[13] B.Q. Guo, I. Babuška, The h-p version of the finite element methods. Part 1. The basic approximation results, Comput. Mech. 1 (1986) 21-41; Part 2. General results and applications, Comput. Mech. 1 (1986) 203-220.
[14] Guo, B.Q.; Babuška, I., On the regularity of elasticity problems with piecewise analytic data, Adv. appl. math., 14, 307-347, (1993) · Zbl 0790.35028
[15] Kellog, R.B.; Osborn, J.E., A regularity for the Stokes problem in a convex polygon, J. funct. anal., 21, 4, 397-431, (1976) · Zbl 0317.35037
[16] V.A. Kondratev, Boundary value problem for parabolic equations in corner domains, Trans. Moscow Math. Soc. (1966) 450-504.
[17] V.A. Kondratev, Boundary value problem for elliptic equations in domain with conic or angular points, Trans. Moscow Math. Soc. (1967) 227-313.
[18] Maz’ya, V.G.; Plamenevskii, B.A., The first boundary value problem for the classical equations of mathematical physics in domains with piecewise smooth boundary parts I and II, Zeitschrift f. analysis und ihre anw., 2, 6, 523-551, (1983), (in Russian) · Zbl 0554.35099
[19] V.G. Maz’ya, B.A. Plamenevskii, Estimates in \(L_p\) and Hölder class and the Miranda-Agmon maximum principle for solutions of elliptic boundary problems in domains with singular points on the boundary, Amer. Math. Soc. Transl. (2) 123 (1984) 1-56.
[20] Morrey, C.B., Multiple integrals in calculus of variations, (1966), Springer Berlin, Heidelberg, New York · Zbl 0142.38701
[21] M. Orlt, Regularitätsuntersuchungen und Fehlerabschätzungen für allgemeine Randwertprobleme der Navier-Stokes Gleichungen, Doctoral Dissertation, Stuttgart University, 1998.
[22] Orlt, M.; Sändig, M., Regularity of viscous navier – stokes flows in nonsmooth domains, (), 185-201 · Zbl 0826.35095
[23] Schwab, C., p- and hp-FEM, (1998), Oxford University Press Oxford · Zbl 1298.74237
[24] Schwab, C.; Suri, M., Mixed hp finite element methods for Stokes and non-Newtonian flow, Comp. methods appl. mech. eng., 175, 217-241, (1999) · Zbl 0924.76052
[25] Stephan, E.P.; Suri, M., On the convergence of the p-version of the boundary element method, Math. comp., 52, 1-48, (1989) · Zbl 0661.65118
[26] Stephan, E.P.; Suri, M., The h-p version of the boundary element method on polygonal domains with quasiuniform meshes, Math. model. numer. anal. (RAIRO), 25, 783-807, (1991) · Zbl 0744.65073
[27] Wahlbin, L.B., On the sharpness of certain local estimates for \(\overset{\mathring{}}{H}^1\) projections into finite element spaces: influence of a reentrant corner, Math. comp., 42, 1-8, (1984) · Zbl 0539.65078
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