Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions

Raymond, J.-P.

doi:10.1016/j.anihpc.2006.06.008

Raymond, J.-P.

Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 921-951.

| 5 citations dans Numdam

DOI : 10.1016/j.anihpc.2006.06.008

@article{AIHPC_2007__24_6_921_0,
     author = {Raymond, J.-P.},
     title = {Stokes and {Navier-Stokes} equations with nonhomogeneous boundary conditions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {921--951},
     publisher = {Elsevier},
     volume = {24},
     number = {6},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.06.008},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2006.06.008/}
}

TY  - JOUR
AU  - Raymond, J.-P.
TI  - Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 921
EP  - 951
VL  - 24
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2006.06.008/
DO  - 10.1016/j.anihpc.2006.06.008
LA  - en
ID  - AIHPC_2007__24_6_921_0
ER  -

%0 Journal Article
%A Raymond, J.-P.
%T Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 921-951
%V 24
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2006.06.008/
%R 10.1016/j.anihpc.2006.06.008
%G en
%F AIHPC_2007__24_6_921_0

Raymond, J.-P. Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 921-951. doi : 10.1016/j.anihpc.2006.06.008. http://archive.numdam.org/articles/10.1016/j.anihpc.2006.06.008/

Bibliographie
Cité par

[1] Amann H., Nonhomogeneous Navier-Stokes equations with integrable low-regularity data, in: Birman , (Eds.), Nonlinear Problems in Mathematical Physics and Related Topics II, Kluwer Academic/Plenum Publishers, New York, 2002, pp. 1-28.

[2] Amann H., Navier-Stokes equations with nonhomogeneous Dirichlet boundary conditions, J. Nonlinear Math. Phys. 10 (Suppl. 1) (2003) 1-11.

[3] V. Barbu, I. Lasiecka, R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations, Mem. Amer. Math. Soc. (2006), in press. | Zbl

[4] Bensoussan A., Da Prato G., Delfour M.C., Mitter S.K., Representation and Control of Infinite Dimensional Systems, vol. 1, Birkhäuser, 1992. | MR | Zbl

[5] Bensoussan A., Da Prato G., Delfour M.C., Mitter S.K., Representation and Control of Infinite Dimensional Systems, vol. 2, Birkhäuser, 1993. | Zbl

[6] Dautray R., Lions J.-L., Analyse Mathématique et Calcul Numérique, vol. 8, Masson, Paris, 1988.

[7] R. Farwig, G.P. Galdi, H. Sohr, A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data, J. Math. Fluid Mech., published on line 27 October 2005. | Zbl

[8] Fursikov A.V., Gunzburger M.D., Hou L.S., Trace theorems for three-dimensional time-dependent solenoidal vector fields and their applications, Trans. Amer. Math. Soc. 354 (2001) 1079-1116. | MR | Zbl

[9] Fursikov A.V., Gunzburger M.D., Hou L.S., Inhomogeneous boundary value problems for the three-dimensional evolutionary Navier-Stokes equations, J. Math. Fluid Mech. 4 (2002) 45-75. | Zbl

[10] Galdi G.P., An Introduction to the Mathematical Theory of the Navier-Stokes Equations, vol. 1, Springer-Verlag, 1994. | Zbl

[11] Galdi G.P., Simader C.G., Sohr H., A class of solutions to the stationary Stokes and Navier-Stokes equations with boundary data in $W^{1 / q, q}$ , Math. Ann. 331 (2005) 41-74. | Zbl

[12] Grisvard P., Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl. 45 (1966) 143-206, and 207-290. | Zbl

[13] Grubb G., Solonnikov V.A., Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods, Math. Scand. 69 (1991) 217-290. | Zbl

[14] Grubb G., Nonhomogeneous Dirichlet Navier-Stokes problems in low regularity $L_{p}$ Sobolev spaces, J. Math. Fluid Mech. 3 (2001) 57-81. | Zbl

[15] He J.-W., Glowinski R., Metcalfe R., Nordlander A., Periaux J., Active control and drag optimization for flow past a circular cylinder, J. Comp. Phys. 163 (2000) 83-117. | MR | Zbl

[16] Lasiecka I., Triggiani R., The regulator problem for parabolic equations with Dirichlet boundary control, Appl. Math. Optim. 16 (1987) 147-168. | MR | Zbl

[17] Lions J.-L., Espaces d'interpolation et domaines de puissances fractionnaires d'opérateurs, J. Math. Soc. Japan 14 (1962) 233-241. | MR | Zbl

[18] Lions J.-L., Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris, 1969. | MR | Zbl

[19] Lions J.-L., Magenes E., Problèmes aux limites non homogènes, vol. 1, Dunod, Paris, 1968. | Zbl

[20] Lions J.-L., Magenes E., Problèmes aux limites non homogènes, vol. 2, Dunod, Paris, 1968. | Zbl

[21] Nguyen P.A., Raymond J.-P., Control problems for convection-diffusion equations with control localized on manifolds, ESAIM Control Optim. Calc. Var. 6 (2001) 467-488. | Numdam | MR | Zbl

[22] Raymond J.-P., Feedback boundary stabilization of the two-dimensional Navier-Stokes equations, SIAM J. Control Optim. 45 (2006) 790-828. | Zbl

[23] Raymond J.-P., Local boundary feedback stabilization of the Navier-Stokes equations, in: Control Systems: Theory, Numerics and Applications, http://pos.sissa.it.

[24] Solonnikov V.A., Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations, in: Amer. Math. Soc. Transl. Ser. 2, vol. 75, 1968, pp. 1-116. | Zbl

[25] Temam R., Navier-Stokes Equations, North-Holland, 1984. | Zbl

[26] Troianiello G.M., Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. | MR | Zbl

[27] Von Wahl W., The Equations of Navier-Stokes and Abstract Parabolic Equations, Vieweg and Sohn, Braunschweig, 1985.

Cité par Sources :