### 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 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.

Original language | English |
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Pages (from-to) | 1035-1058 |

Number of pages | 24 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 20 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2018 Sep 1 |

### Keywords

- Brinkman–Forchheimer equation
- Double-diffusive convection
- Large data
- Time periodic problem
- Whole space domain

### ASJC Scopus subject areas

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics

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## Cite this

Otani, M., & Uchida, S. (2018). Existence of Time Periodic Solution to Some Double-Diffusive Convection System in the Whole Space Domain.

*Journal of Mathematical Fluid Mechanics*,*20*(3), 1035-1058. https://doi.org/10.1007/s00021-017-0354-1