Time-periodic solutions of the primitive equations of large-scale moist atmosphere: existence and stability

References

• Lions JL, Temam R, Wang S. New formulations of the primitive equations of atmosphere and applications. Nonlinearity. 1992;5:237–288.
   Web of Science ®Google Scholar
• Temam R, Ziane M. Some mathematical problems in geophysical fluid dynamics. In: Friedlander S, Serre D, editors. Handbook of mathematical fluid dynamics. Amsterdam: North-Holland; 2004. p. 535–657.
   Google Scholar
• Cao C, Titi ES. Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Ann. Math. 2007;166:245–267.
   Web of Science ®Google Scholar
• Kobelkov GM. Existence of a solution “in the large” for the 3d large-scale ocean dynamics equations. J. Math. Fluid Mech. 2007;9:588–610.
   Web of Science ®Google Scholar
• Guo B, Huang D. Existence of weak solutions and trajectory attractors for the moist atmospheric equations in geophysics. J. Math. Phys. 2006;47:22 pp.
   Google Scholar
• Guo B, Huang D. Existence of the universal attractor for the 3-d viscous primitive equations of large-scale moist atmosphere. J. Differ. Equ. 2011;251:457–491.
   Web of Science ®Google Scholar
• Serrin J. A note on the existence of periodic solutions of the Navier–Stokes equations. Arch. Ration. Mech. Anal. 1959;3:120–122.
   Web of Science ®Google Scholar
• Serrin J. On the stability of viscous fluid motions. Arch. Ration. Mech. Anal. 1959;3:1–13.
   Web of Science ®Google Scholar
• Kaniel S, Shinbrot M. A reproductive property of the Navier–Stokes equations. Arch. Ration. Mech. Anal. 1967;24:363–369.
   Web of Science ®Google Scholar
• Takeshita A. On the reproductive property of the 2-dimensional Navier–Stokes equations. J. Fac. Sci., Univ. Tokyo. Sect. IA. Math. 1970;16:297–311.
   Web of Science ®Google Scholar
• Kucera P. The time-periodic solutions of the Navier–Stokes equations with mixed boundary conditions. Discrete Contin. Dyn. Syst. Ser. S. 2010;3:325–337.
   Google Scholar
• Kato H. Existence of periodic solutions of the Navier–Stokes equations. J. Math. Anal. Appl. 1997;208:141–157.
   Web of Science ®Google Scholar
• Beirao da Veiga H. Time-periodic solutions of the Navier–Stokes equations in unbounded cylindrical domains – Lerays problem for periodic flows. Arch. Ration. Mech. Anal. 2005;178:301–325.
   Web of Science ®Google Scholar
• Galdi G, Sohr H. Existence and uniqueness of time-periodic physically reasonable Navier–Stokes flow past a body. Arch. Ration. Mech. Anal. 2004;172:363–406.
   Web of Science ®Google Scholar
• Maremonti P. Existence and stability of time-periodic solutions to the Navier–Stokes equations in the whole space. Nonlinearity. 1991;4:503–529.
   Web of Science ®Google Scholar
• Taniuchi Y. On the uniqueness of time-periodic solutions to the Navier–Stokes equations in unbounded domains. Math. Z. 2009;261:597–615.
   Web of Science ®Google Scholar
• Tachim Medjo T. Existence and uniqueness of strong periodic solutions of the Primitive equations of the ocean. Discrete Contin. Dyn. Syst. 2010;26:1491–1508.
   Web of Science ®Google Scholar
• Hsia C-H, Shiue M-C. On the asymptotic stability analysis and the existence of time-periodic solutions of the primitive equations. Indiana Univ. Math. J. 2013;62:403–441.
   Web of Science ®Google Scholar
• Lions JL, Temam R, Wang S. Models of the coupled atmosphere and ocean (cao i). Comput. Mech. Adv. 1993;1:1–54.
   Google Scholar
• Foias C, Prodi G. Sur le comportement global des solutions non-stationnaires des’equations de Navier–Stokes en dimension 2. Rend. Sem. Mat. Univ. Padova. 1967;39:1–34.
   Google Scholar
• Temam R. Infinite dimensional dynamical systems in mechanics and physics. 2nd ed. New York (NY): Spring-Verlag; 1997.
   Google Scholar
• Adams RA. Sobolev spaces. New York (NY): Academic Press; 1975.
   Google Scholar
• Constantin P, Foias C. Navier–Stokes equations. Chicago (IL): The University of Chicago Press; 1988.
   Google Scholar
• Galdi GP. An introduction to the mathematical theory of the Navier–Stokes equations. Vol. I. New York (NY): Springer-Verlag; 1994.
   Google Scholar
• Ladyzhenskaya OA. The boundary value problems of mathematical physics. New York (NY): Springer-Verlag; 1985.
   Google Scholar
• Cao C, Titi ES. Global well-posedness and finite-dimensional global attractor for a 3-d planetary geostrophic viscous model. Comm. Pure Appl. Math. 2003;56:198–233.
   Web of Science ®Google Scholar
• Petcu M, Temam R, Ziane M. Some mathematical problems in geophysical fluid dynamics. In: Ciarlet PG, editor. Handbook of numerical analysis, special volume on computational methods for the oceans and the atmosphere. Vol. XIV. New York (NY): Elsevier; 2008. p. 577–750.
   Google Scholar
• Ju N. The global attractor for the solutions to the 3d viscous primitive equations. Discrete Contin. Dyn. Syst. 2007;17:159–179.
   Web of Science ®Google Scholar