Geodesic
Stability of steady-states solution to Navier–Stokes equations with general Navier slip boundary condition
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 153-175 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Steady solution and asymptotic behaviour of corresponding nonsteady solution are studied for the Navier–Stokes equations under general Navier slip boundary condition. It is proved the existence of a unique stationary solution and that this solution is asymptotically stable under some restrictions on the data. Bibl. – 16 titles. 
@article{ZNSL_2008_362_a6,
     author = {Sh. Itoh and N. Tanaka and A. Tani},
     title = {Stability of steady-states solution to {Navier{\textendash}Stokes} equations with general {Navier} slip boundary condition},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {153--175},
     year = {2008},
     volume = {362},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a6/}
}
TY  - JOUR
AU  - Sh. Itoh
AU  - N. Tanaka
AU  - A. Tani
TI  - Stability of steady-states solution to Navier–Stokes equations with general Navier slip boundary condition
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2008
SP  - 153
EP  - 175
VL  - 362
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a6/
LA  - en
ID  - ZNSL_2008_362_a6
ER  - 
%0 Journal Article
%A Sh. Itoh
%A N. Tanaka
%A A. Tani
%T Stability of steady-states solution to Navier–Stokes equations with general Navier slip boundary condition
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 153-175
%V 362
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a6/
%G en
%F ZNSL_2008_362_a6
Sh. Itoh; N. Tanaka; A. Tani. Stability of steady-states solution to Navier–Stokes equations with general Navier slip boundary condition. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 153-175. http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a6/

[1] S. Agmon, A. Douglis, L. Nirenberg,, “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I”, Comm. Pure Appl. Math., 12 (1959), 623–727 ; “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II”, 17 (1964), 35–92 | DOI | MR | Zbl | DOI | MR | Zbl

[2] R. Farwig, “Stationary solutions of compressible Navier–Stokes equations with slip boundary condition”, Comm. Partial Differential Equations, 14 (1989), 1579–1606 | DOI | MR | Zbl

[3] G. P. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations. Vol. I. Linearized Steady Problems, Springer, Heiderberg–New York, 1994 | MR

[4] S. Goldstein (ed.), Modern Developments in Fluid Dynamics, Vol. 2, Dover, New York, 1965

[5] S. Itoh, N. Tanaka, A. Tani, “The initial value problem for the Navier–Stokes equations with general slip boundary condition in Hölder spaces”, J. Math. Fluid Mech., 5 (2003), 275–301 | MR | Zbl

[6] S. Itoh, A. Tani, “The initial value problem for the non-homogeneous Navier–Stokes equations with general slip boundary condition”, Proc. Roy. Soc. Edinburgh Sect. A, 130 (2000), 827–835 | DOI | MR | Zbl

[7] O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Second English edition, Gordon and Breach, 1969 | MR | Zbl

[8] C. L. M. H. Navier, “Mémoire sur les lois du mouvement des fluides”, Mém. Acad. Sci. Inst. France, 6 (1823), 389–440

[9] V. V. Pukhnachov, “Plane steady-state problem with a free boundary for the Navier–Stokes equations”, Zh. Prikl. Mech. Techn. Fiz., 13 (1972), 91–102

[10] J. Serrin, “Mathematical principles of classical fluid mechanics”, Handbuch der Physik, VIII/1, Springer, Berlin, 1959, 125–263 | MR

[11] V. A. Solonnikov, “General boundary value problems for systems elliptic in the sence of A. Douglis and L. Nirenberg. I”, Amer. Math. Soc. Transl. (2), 56 (1966), 193–232 ; “General boundary value problems for systems elliptic in the sence of A. Douglis and L. Nirenberg. II”, Proc. Steklov Inst. Math., 92, 1968, 269–339 | MR | Zbl

[12] V. A. Solonnikov, “Unsteady motion of a finite mass of fluid, bounded by a free surface”, J. Soviet Math., 40 (1988), 672–686 | DOI | MR | Zbl

[13] V. A. Solonnikov, V. E. Sčadilov, “On a boundary value problem for a stationary system of Navier–Stokes equations”, Proc. Steklov Inst. Math., 125, 1973, 196–210 | MR | Zbl

[14] A. Tani, S. Itoh, N. Tanaka, “The initial value problem for the Navier–Stokes equations with general slip boundary condition”, Adv. Math. Sci. Appl., 4 (1994), 51–69 | MR | Zbl

[15] A. Tani, “The initial value problem for the equations of motion of general fluid with general slip boundary condition”, Kôkyuroku, RIMS (Kyoto Univ.), 734 (1990), 123–142 | MR

[16] L. R. Volevic, “Solvability of boundary value problem for general elliptic systems”, Amer. Math. Soc. Transl. (2), 67 (1968), 182–225 | Zbl