Geodesic
Projection and projection-difference methods for the solution of the Navier–Stokes equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 898-912 
P. V. Vinogradova; A. G. Zarubin; J. O. Suetina. Projection and projection-difference methods for the solution of the Navier–Stokes equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 898-912. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a11/
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     title = {Projection and projection-difference methods for the solution of the {Navier{\textendash}Stokes} equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The projection and projection-difference methods for the approximate solution of the nonlinear unsteady Navier–Stokes equations in a bounded two-dimensional region are studied. Asymptotic estimates for the convergence rate of the approximate solutions and the time and space derivatives in the uniform topology are obtained.

[1] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970

[2] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981

[3] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972

[4] Kopachevskii N. D., Krein S. G., Ngo Zui Kan, Operatornye metody v lineinoi gidrodinamike. Evolyutsionnye i spektralnye zadachi, Nauka, M., 1989

[5] Babskii V. G., Kopachevskii N. D., Myshkis A. D. i dr., Gidrodinamika nevesomosti, Nauka, M., 1976

[6] Glushko V. P., Krain S. G., “Neravenstva dlya norm proizvodnykh v prostranstvakh $L_p$ s vesom”, Sibirskii matem. zhurnal, 1:3 (1960), 343–382

[7] Bekkenbakh F., Bellman R., Neravenstva, Mir, M., 1965

[8] Solonnikov V. A., “Ob otsenkakh v $L_q$ reshenii ellipticheskikh i parabolichesikkh sistem”, Tr. MIAN SSSR, 11, no. 5, 1967, 137–160

[9] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967

[10] Vinogradova P., Zarubin A., “Projection method for Cauchy problem for an operator differential equation”, Numer. Functional Analysis and Optimizat., 30:1 (2009), 148–167

[11] Demidovich V. B., “Ob asimptoticheskom povedenii reshenii konechno-raznostnykh uravnenii”, Differents. ur-niya, 10:12 (1974), 2267–2278