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Existence of a Global Solution to One Model Problem of Atmosphere Dynamics

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Abstract

We consider a model problem of compressible viscous fluid dynamics in the two-dimensional case. We prove a global existence theorem.

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References

  1. Min Lu, Kazhikhov A. V., and Ukai Seiji, “Global solutions to the Cauchy problem of the Stokes approximation equations for two-dimensional compressible flow,” Sci. Bull. Josai Univ. Spec. Iss., No. 5, 155–174 (1998).

  2. Lions P.-L., Mathematical Topics in Fluid Mechanics. Compressible Models. Vol. 2, Oxford Univ. Press, Oxford (1998).

    Google Scholar 

  3. Lewandowski R., Analyse Mathematique et Oceanographie, Masson (1997).

  4. Kochin N. E., “On simplification of the equations of hydromechanics in the case of the general circulation of the atmosphere,” Trudy Glavn. Geofiz. Observator., 4, 21–45 (1936).

    Google Scholar 

  5. Antontsev S. N., Kazhikhov A. V., and Monakhov V. N., Boundary Value Problems of Inhomogeneous Fluid Mechanics [in Russian], Nauka, Novosibirsk (1983).

    Google Scholar 

  6. Nash J., “Le probleme de Cauchy pour les equations differentielles d'un fluide general,” Bull. Soc. Math. France, 90, No.4, 487–491 (1962).

    Google Scholar 

  7. Matsumura A. and Nishida T., “The initial value problem for the equation of motion of viscous and heat-conductive gases,” J. Math. Kyoto Univ., 20, No.1, 67–104 (1980).

    Google Scholar 

  8. Brech D., Gullen-Gonzales F., Masmoudi N., and Rodrigues-Bellido M. A., “On the uniqueness for the two-dimensional primitive equation,” Differential Integral Equations, 16, No.1, 77–94 (2001).

    Google Scholar 

  9. Bresch D., Kazhikhov A., and Lemoine J., “On the two-dimensional hydrostatic Navier-Stokes equations,” SIAM J. Math. Anal., 36, No.3, 796–814 (2004).

    Article  MathSciNet  Google Scholar 

  10. Gullen-Gonzales F., Masmoudi N., and Rodrigues-Bellido M. A., “Anisotropic estimates and strong solutions of the primitive equations,” Differential Integral Equations, 14, No.11, 1381–1400 (2001).

    Google Scholar 

  11. Ladyzhenskaya O. A. and Ural'tseva N. N., Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).

    Google Scholar 

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Authors and Affiliations

  1. Lavrent'ev Institute of Hydrodynamics, Novosibirsk, Russia

    B. V. Gatapov & A. V. Kazhikhov

Authors
  1. B. V. Gatapov
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  2. A. V. Kazhikhov
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Dedicated to a blessed memory of Tadei Ivanovich Zelenyak.

Original Russian Text Copyright © 2005 Gatapov B. V. and Kazhikhov A. V.

The authors were supported by the Russian Foundation for Basic Research (Grant 05-01-00131).

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 1011–1020, September– October, 2005.

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Gatapov, B.V., Kazhikhov, A.V. Existence of a Global Solution to One Model Problem of Atmosphere Dynamics. Sib Math J 46, 805–812 (2005). https://doi.org/10.1007/s11202-005-0079-x

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  • DOI: https://doi.org/10.1007/s11202-005-0079-x

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