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Existence of Time Periodic Solution to Some Double-Diffusive Convection System in the Whole Space Domain

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Abstract

This paper is concerned with the existence of time periodic solutions to some system which describes double-diffusive convection phenomena in the whole space \({\mathbb {R}} ^N \) with \(N = 3\) and 4. In previous results for periodic problems of parabolic type equations with non-monotone perturbation terms, it seems that either of the smallness of given data or the boundedness of space domain is essential. In spite of the presence of non-monotone terms, the solvability of our problem in the whole space is shown for large external forces via the convergence of solutions to approximate equations in bounded domains.

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Acknowledgements

The authors would like to thank the editor and the referees for carefully reading the manuscript and for giving constructive comments which substantially helped improving the quality of this paper. The first author was partially supported by the Grant-in-Aid for Scientific Research [Grant Number 15K13451], the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. The second author was supported by the Grant-in-Aid for JSPS Fellows [Grant Number 26\(\cdot \)5316], Japan Society for the Promotion of Science (JSPS). Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Department of Applied Physics, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku, Tokyo, 169-8555, Japan

    Mitsuharu Ôtani & Shun Uchida

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  1. Mitsuharu Ôtani
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  2. Shun Uchida
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Correspondence to Shun Uchida.

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Communicated by Y. Shibata.

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Ôtani, M., Uchida, S. Existence of Time Periodic Solution to Some Double-Diffusive Convection System in the Whole Space Domain. J. Math. Fluid Mech. 20, 1035–1058 (2018). https://doi.org/10.1007/s00021-017-0354-1

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  • DOI: https://doi.org/10.1007/s00021-017-0354-1

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