Solving the linear Rossby equation in a finite domain
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 142-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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We state a generalized formulation for the first and the second initial-boundary value problems for the Rossby equation and prove the unique solvability of these problems. For the first initial-boundary value problem, the approximate solution is constructed. The convergence rate to the generalized solution is studied. The results of the numerical experiments are discussed.
Keywords: Rossby equation, planetary wave equation.
Mots-clés : Sobolev-type equations
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A. A. Svidlov. Solving the linear Rossby equation in a finite domain. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 142-149. http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a13/

[1] Brekhovskikh L. M., Goncharov V. V., Vvedenie v mekhaniku sploshnykh sred, Nauka, M., 1982, 335 pp.

[2] Biryuk A., “Lower bounds for derivatives of solutions for nonlinear Schrödinger equations”, Proc. R. Soc. Edinb. Sect. A, Math., 139:2 (2009), 237–251 | DOI | MR | Zbl

[3] Rossby C.-G., “On the dispersion of planetary waves in a barotropic atmosphere”, Tellus, 1:1 (1949), 54–58 | DOI | MR

[4] Uspenskii S. V., Demidenko G. V., “O povedenii pri $t\to\infty$ reshenii nekotorykh zadach gidrodinamiki”, Dokl. RAN, 280:5 (1985), 1072–1075 | MR

[5] Tikilyainen A. A., “Ob odnoi zadache, svyazannoi s teoriei planetarnykh voln”, Zhurn. vychisl. matem. i matem. fiziki, 28:4 (1988), 534–548 | MR | Zbl

[6] Ogorodnikov I. E., Stabilizatsiya resheniya uravneniya planetarnykh voln v neogranichennykh po prostranstvennym peremennym oblastyakh, Dis. $\dots$ kand. fiz.-matem. nauk, M., 2000, 101 pp.

[7] Ilin A. M., “O povedenii resheniya odnoi kraevoi zadachi pri $t\to\infty$”, Matem. sbornik, 87(129):4 (1972), 529–553 | MR | Zbl

[8] Lezhnëv V. G., Asimptoticheskie zadachi lineinoi gidrodinamiki, Izd-vo KubGU, Krasnodar, 1993, 92 pp.

[9] Svidlov A. A., Biryuk A. E., Drobotenko M. I., “Negladkoe reshenie uravneniya Rossbi”, Ekol. vestn. nauch. tsentrov ChES, 2013, no. 2, 89–94

[10] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983, 401 pp. | MR | Zbl

[11] Trenogin V. A., Funktsionalnyi analiz, Fizmatlit, M., 2002, 488 pp.

[12] Kupradze V. D., “O priblizhennom reshenii zadach matematicheskoi fiziki”, Usp. matem. nauk, 22:2 (1967), 59–107 | MR | Zbl

[13] Drobotenko M. I., Ignatev D. V., “Metod tochechnykh potentsialov dlya uravneniya Laplasa”, Ekol. vestn. nauch. tsentrov ChES, 2007, no. 1, 5–9

[14] Mikhlin S. G., Lineinye differentsialnye uravneniya v chastnykh proizvodnykh, Vyssh. shk., M., 1977, 432 pp. | MR

[15] Svidlov A. A., “O vtoroi nachalno-kraevoi zadache dlya uravneniya Rossbi v ogranichennoi oblasti”, Ekol. vestn. nauch. tsentrov ChES, 2009, no. 3, 80–84