Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

[1]Grassberger, P. (1986). Do Climatic Attractors Exist?. Nature, 323, 609–612.GrassbergerP.1986Do Climatic Attractors Exist?Nature32360961210.1038/323609a0Search in Google Scholar

[2]Helgason, S. (1984) Groups and Geometric Analysis. Integral Geometry, Invariant Differential Operators and Spherical Functions. Academic Press, Orlando.HelgasonS.1984Groups and Geometric Analysis. Integral Geometry, Invariant Differential Operators and Spherical FunctionsAcademic PressOrlandoSearch in Google Scholar

[3]Ilyin, A.A. (1993). On the dimension of attractors for Navier-Stokes equations on two-dimensional compact manifolds. Diff. Integr. Equations, 6(1), 183–214.IlyinA.A.1993On the dimension of attractors for Navier-Stokes equations on two-dimensional compact manifoldsDiff. Integr. Equations6118321410.57262/die/1371214986Search in Google Scholar

[4]Ilyin, A.A., Filatov, A.N. (1987). Navier-Stokes equations on a sphere and their unique solvability. The stability of steady solutions. In: Mathematical Physics. Leningrad Pedagogical Institute, Leningrad, pp.128–145. (in Russian)IlyinA.A.FilatovA.N.1987Navier-Stokes equations on a sphere and their unique solvability. The stability of steady solutionsIn:Mathematical PhysicsLeningrad Pedagogical InstituteLeningrad128145(in Russian)Search in Google Scholar

[5]Ilyin, A.A., Filatov, A.N. (1988). On unique solvability of Navier-Stokes equations on two-dimensional sphere. Dokl. Akad. Nauk SSSR, 301(1), 18–22.IlyinA.A.FilatovA.N.1988On unique solvability of Navier-Stokes equations on two-dimensional sphereDokl. Akad. Nauk SSSR30111822Search in Google Scholar

[6]Ladyzhenskaya, O.A. (1969). The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New York.LadyzhenskayaO.A.1969The Mathematical Theory of Viscous Incompressible FlowGordon and BreachNew YorkSearch in Google Scholar

[7]Neven, E.C. (1994). Modons in shear flow on a sphere. Geophys. Astrophys. Fluid Dyn, 74, 51–71.NevenE.C.1994Modons in shear flow on a sphereGeophys. Astrophys. Fluid Dyn74517110.1080/03091929408203632Search in Google Scholar

[8]Richtmyer, R.D. (1978). Principles of Advanced Mathematical Physics. Vol. 1 (1978), Vol. 2 (1981), Springer-Verlag, New York.RichtmyerR.D.1978Principles of Advanced Mathematical PhysicsVol. 1 (1978), Vol. 2 (1981),Springer-VerlagNew York10.1007/978-3-642-46378-5Search in Google Scholar

[9]Samoilenko, A.M. (1991). Elements of the Mathematical Theory of Multi-Frequency Oscillations. Kluwer, Dordrecht.SamoilenkoA.M.1991Elements of the Mathematical Theory of Multi-Frequency OscillationsKluwerDordrecht10.1007/978-94-011-3520-7Search in Google Scholar

[10]Skiba, Yu.N. (1988). Unique Solvability of the Barotropic Vorticity Equation for a Viscous Fluid in Classes of Generalized Functions on the Sphere. Depart. Numer. Mathematics, Akad. Nauk SSSR, VINITI, Moscow, 194, 56 pp. (in Russian)SkibaYu. N.1988Unique Solvability of the Barotropic Vorticity Equation for a Viscous Fluid in Classes of Generalized Functions on the SphereDepart. Numer. Mathematics, Akad. Nauk SSSRVINITIMoscow19456(in Russian)Search in Google Scholar

[11]Skiba, Yu.N. (2012). On the existence and uniqueness of solution to problems of fluid dynamics on a sphere. J. Math. Analys. Appl, 388, 627–644.SkibaYu. N.2012On the existence and uniqueness of solution to problems of fluid dynamics on a sphereJ. Math. Analys. Appl38862764410.1016/j.jmaa.2011.10.045Search in Google Scholar

[12]Skiba, Yu.N. (2018). On Lyapunov and exponential stability of Rossby-Haurwitz waves in invariant sets of perturbations. J. Math. Fluid Mech, 20(3), 1137–1154.SkibaYu. N.2018On Lyapunov and exponential stability of Rossby-Haurwitz waves in invariant sets of perturbationsJ. Math. Fluid Mech2031137115410.1007/s00021-017-0359-9Search in Google Scholar

[13]Sundstrëm, A. (1969). Stability theorems for the barotropic vorticity equations. Mon. Wea. Rev., 97(4), 340–345.SundstrëmA.1969Stability theorems for the barotropic vorticity equationsMon. Wea. Rev.97434034510.1175/1520-0493(1969)097<0340:STFTBV>2.3.CO;2Search in Google Scholar

[14]Temam, R. (1985). Attractors for Navier-Stokes equations. Res. Not. Mat., 122, 272–292.TemamR.1985Attractors for Navier-Stokes equationsRes. Not. Mat.122272292Search in Google Scholar

[15]Verkley, W.T.M. (1987). Stationary barotropic modons in westerly background flows. J. Atmos. Sci., 44, 2383–2398.VerkleyW.T.M.1987Stationary barotropic modons in westerly background flowsJ. Atmos. Sci.442383239810.1175/1520-0469(1987)044<2383:SBMIWB>2.0.CO;2Search in Google Scholar