Geodesic
Stability theory for a two-dimensional channel
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1331-1346 Cet article a éte moissonné depuis la source Math-Net.Ru

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A scheme for deriving conditions for the nonlinear stability of an ideal or viscous incompressible steady flow in a two-dimensional channel that is periodic in one direction is described. A lower bound for the main factor ensuring the stability of the Reynolds–Kolmogorov sinusoidal flow with no-slip conditions (short wavelength stability) is improved. A condition for the stability of a vortex strip modeling Richtmyer–Meshkov fluid vortices (long wavelength stability) is presented. 
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O. V. Troshkin. Stability theory for a two-dimensional channel. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1331-1346. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a8/

[1] Gurvits A., Kurant R., Teoriya funktsii, Nauka, M., 1968, 648 pp.

[2] Troshkin O. V., “K teorii periodicheskogo sloya neszhimaemoi zhidkosti”, Zh. vychisl. matem. i matem. fiz., 47:4 (2007), 738–744 | Zbl

[3] Troshkin O. V., ““Transportnaya” forma uravnenii periodicheskogo sloya neszhimaemoi sredy”, Dokl. AN, 419:6 (2008), 739–743 | Zbl

[4] Wolibmr W., “On theoreme sur l'existence du movement plan d'un fluid parfait, homogene, incompressible, pendant um temps infiniment longue”, Math. Z., 37 (1933), 698–726 | DOI | MR

[5] Kato T., “On classical solutions of the two dimensional nonstationary Euler equations”, Arch. Rat. Mech. Anal., 25:3 (1967), 188–200 | DOI | MR | Zbl

[6] Yudovich V. I., “Dvumernaya nestatsionarnaya zadacha protekaniya idealnoi zhidkosti cherez zadannuyu oblast”, Matem. sb., 64 (1964), 562–588

[7] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970, 288 pp.

[8] Jacobs J. W., Jones M. A., Niederhaus C. E., “Experimental studies of Richtvyer–Meshkov instability”, Proc. Fifth Internat. Workshop on Compressible Turbulent Mixing, eds. R. Young, J. Glimm, B. Boston, World Sci., 1996, 195–202 | MR

[9] Troshkin O. V., “Dvumernaya zadacha o protekanii dlya statsionarnykh uravnenii Eilera”, Matem. sb., 180:3 (1989), 354–374

[10] Troshkin O. V., “O topologicheskom analize struktury gidrodinamicheskikh techenii”, Uspekhi matem. nauk, 43:4(262) (1988), 129–158

[11] Reynolds O., “An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels”, Phil. Trans. R. Soc. Lond., 174 (1883), 935–982 | DOI

[12] Lin Tszya-tszyao, Teoriya gidrodinamicheskoi ustoichivosti, Izd-vo inostr. lit., M., 1974, 194 pp.

[13] Arnold V. I., Meshalkin A. D., Seminar A. N., “Kolmogorova po izbrannym voprosam analiza (1958–1959)”, Uspekhi matem. nauk, 15:1 (1960), 247–250

[14] Troshkin O. V., “Algebraicheskaya struktura dvumernykh statsionarnykh uravnenii Nave-Stoksa i nelokalnye teoremy edinstvennosti”, Dokl. AN SSSR, 298:6 (1988), 1372–1376 | Zbl

[15] Troshkin O. V., “K nelineinoi ustoichivosti parabolicheskogo profilya v ploskom periodicheskom kanale”, Zh. vychisl. matem. i matem. fiz., 53:11 (2013), 142–161

[16] Aleshin A. N., Gamalii E. G., Zaitsev S. G., Lazareva E. V., Lebo I. G., Rozanov V. B., “Issledovanie nelineinoi i perekhodnoi stadii razvitiya neustoichivosti Rikhtmaiera-Meshkova”, Pisma v ZhTF, 12:12 (1988), 1063–1067

[17] Krylov A. L., “Ob ustoichivosti techeniya Puazeilya v ploskom kanale”, Dokl. AN SSSR, 159:5 (1964), 978–981

[18] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, GITTL, M., 1956, 392 pp.

[19] Yudovich V. I., Metod linearizatsii v gidrodinamicheskoi teorii ustoichivosti, RGU, Rostov-na-Donu, 1984, 192 pp.

[20] Arnold V. I., “Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydro-dynamique de fluids parfaits”, Ann. Inst. Fourier (Grenoble), 16 (1966), 319–361 | DOI | MR | Zbl

[21] Belotserkovskii O. M., Konyukhov A. V., Oparin A. M., Troshkin O. V., Fortova S. V., “O strukturirovanii khaosa”, Zh. vychisl. matem. i matem. fiz., 51:2 (2011), 237–250 | Zbl