Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension

Chérif Amrouche; Vivette Girault

Czechoslovak Mathematical Journal (1994)

  • Volume: 44, Issue: 1, page 109-140
  • ISSN: 0011-4642

How to cite

top

Amrouche, Chérif, and Girault, Vivette. "Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension." Czechoslovak Mathematical Journal 44.1 (1994): 109-140. <http://eudml.org/doc/31399>.

@article{Amrouche1994,
author = {Amrouche, Chérif, Girault, Vivette},
journal = {Czechoslovak Mathematical Journal},
keywords = {Stokes problem; existence of the solution; Helmholtz decomposition},
language = {eng},
number = {1},
pages = {109-140},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension},
url = {http://eudml.org/doc/31399},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Amrouche, Chérif
AU - Girault, Vivette
TI - Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
JO - Czechoslovak Mathematical Journal
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 1
SP - 109
EP - 140
LA - eng
KW - Stokes problem; existence of the solution; Helmholtz decomposition
UR - http://eudml.org/doc/31399
ER -

References

top
  1. Sobolev Spaces, Academic Press, New York, 1975. (1975) Zbl0314.46030MR0450957
  2. 10.1002/cpa.3160120405, Comm. Pure Appl. Math. 12 (1959), 623–727. (1959) MR0125307DOI10.1002/cpa.3160120405
  3. 10.1002/cpa.3160170104, Comm. Pure Appl. Math. 17 (1964), 35–92. (1964) MR0162050DOI10.1002/cpa.3160170104
  4. Propriétés d’opérateurs de dérivation. Application au problème non homogène de Stokes, CRAS 310 Série I (1990), 367–370. (1990) Zbl0698.46035MR1046514
  5. On the existence and regularity of the solution of the Stokes problem in arbitrary dimension, Proc. of the Japan Ac. 67 Ser. A (1991), no. 5, 171–175. (1991) MR1114965
  6. Propriétés fonctionnelles d’opérateurs, Application au problème de Stokes en dimension quelconque, Report n. 90025, LAN-UPMC, 1990. (1990) 
  7. Problèmes généralisés de Stokes, Potugal. Math. 49 4 (1992), 463–503. (1992) MR1300580
  8. 10.1007/BF01436561, Numer. Math. 20 (1973), 179–192. (1973) MR0359352DOI10.1007/BF01436561
  9. Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl. 20 (1979), 1094–1098. (1979) MR0553920
  10. Solution of some vector analysis problems connected with operators d i v and g r a d , Trudy Seminar, N.L. Sobolev, 80 (1980), no. 1, Akademia Nauk SSSR, Sibirskoe Otdelenie Matematiki, Novosibirsk, 5–40. (Russian) (1980) MR0631691
  11. 10.14492/hokmj/1381517172, Hokkaido Math. J. 19 (1990), 67–87. (1990) MR1039466DOI10.14492/hokmj/1381517172
  12. On the existence, uniqueness and approximation of saddle-points problems arising from Lagrange multipliers, R.A.I.R.O., Anal. Numer. R2 (1974), 129–151. (1974) MR0365287
  13. Su un problema al contorno relativo al sistema di equazoni di Stokes, Rend. Sem. Univ. Padova 31 (1961), 308–340. (1961) MR0138894
  14. Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, vol. 3 and vol. 7, Masson, 1988. (1988) 
  15. An 𝐋 r -theorem of the Helmholtz decomposition of vector fields, J. Fac. Sci. Univ. Tokyo 24 (1977), 685–700. (1977) MR0492980
  16. 10.1007/BF02384076, Arch. Rat. Mech. Anal. 112 (1990), 291–318. (1990) MR1077262DOI10.1007/BF02384076
  17. 10.1007/BF02414374, Ann. Mat. Pura Appl. (4) 69 (1965), 207–284. (1965) MR0196262DOI10.1007/BF02414374
  18. 10.1080/03605308408820363, C. P.D.E. (9) 13 (1984), 1265–1298. (1984) Zbl0602.35093MR0764664DOI10.1080/03605308408820363
  19. Analyticity of the semigroup generated by the Stokes operator in L r spaces, Zeitschrift, (1981), 297–329. (1981) Zbl0473.35064MR0635201
  20. Finite Element Methods for Navier-Stokes Equations, Springer Series SCM, 1986. (1986) MR0851383
  21. Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Math., vol. 24, Pitman, 1985. (1985) MR0775683
  22. 10.1080/03605308108820212, C.P.D.E. 6 (12) (1981), 1301–1334. (1981) MR0640159DOI10.1080/03605308108820212
  23. L q -regularity theory of the Stokes equations in exterior domains, Preprint, Universität Paderborn, 1981. (1981) 
  24. Quelques Méthodes de Résolution des Problèmes aux Limites Non-Linéaires, Gauthier-Villars, 1969. (1969) Zbl0189.40603MR0259693
  25. Problemi ai limiti non homogenei (III), Ann. Scuola Norm. Sup. Pisa 15 (1961), 41–103. (1961) MR0146526
  26. I problemi al contorno per le equazioni di tipo ellittico, Ann. Scuola. Norm. Sup. Pisa. 12 (1958), 247–357. (1958) MR0123818
  27. Equations aux Dérivées Partielles, Presses de l’Univ. de Montréal, 1966. (1966) 
  28. Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967. (1967) MR0227584
  29. 10.5802/aif.232, Annales de l’Institut Fourier 16 (1966), 279–317. (1966) MR0221282DOI10.5802/aif.232
  30. Variétés Différentiables, Hermann, 1960. (1960) 
  31. Primitives de distributions et applications, Séminaire d’Analyse, Clermont-Ferrand, 1992. (1992) 
  32. Private Communication, . 
  33. Estimates in L p of solutions of elliptic and parabolic systems, Proc. Steklov Inst. Math. 102 (1967), 157–185. (1967) MR0228809
  34. Nonlinear Partial Differential Equations using Compactness Methods, Report 1584, Mathematics Research Center, Univ. of Wisconsin, Madison, 1975. (1975) 
  35. Topics in Non Linear Analysis, Publications Mathématiques d’Orsay, 1978. (1978) 
  36. Introduction to Functional Analysis, Wiley, New York, 1958. (1958) Zbl0081.10202MR0098966
  37. Navier-Stokes Equations. Theory and Analysis, North-Holland, Amsterdam, 1985. (1985) MR0603444
  38. Vorlesung über das Aussenraumproblem für die Instationären Gleichungen von Navier-Stokes, vol. 11, Sonderforschungsbereich 256. Nichtlineare Partielle Differentialgleichungen, 1989. (1989) 
  39. Functional Analysis, Springer-Verlag, Berlin, 1965. (1965) Zbl0126.11504
  40. Periodic solutions of viscous incompressible fluids, Dokl. Akad. Nauk SSSR 130 (1960), . (1960) 

Citations in EuDML Documents

top
  1. Ruikuan Liu, Jiayan Yang, Global strong solutions of a 2-D new magnetohydrodynamic system
  2. Václav Mácha, Partial regularity of solution to generalized Navier-Stokes problem
  3. F. Guillén-González, M. A. Rodríguez-Bellido, M. A. Rojas-Medar, Hydrostatic Stokes equations with non-smooth data for mixed boundary conditions
  4. Marc Briane, Nicoletta Tchou, Fibered microstructures for some nonlocal Dirichlet forms
  5. Nguyen Duc Huy, Jana Stará, On existence and regularity of solutions to a class of generalized stationary Stokes problem
  6. Stéphane Busse, Philippe G. Ciarlet, Bernadette Miara, Justification d'un modèle linéaire bi-dimensionnel de coques «faiblement courbées» en coordonnées curvilignes
  7. Marc Briane, Juan Casado-Díaz, Estimate of the pressure when its gradient is the divergence of a measure. Applications
  8. Petr Kaplický, Jakub Tichý, Boundary regularity of flows under perfect slip boundary conditions
  9. Marc Briane, Juan Casado-Díaz, Estimate of the pressure when its gradient is the divergence of a measure. Applications
  10. Martin Lanzendörfer, Jan Stebel, On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.