### 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 |
---|---|

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 |

### Fingerprint

### 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

### Cite this

**Existence of Time Periodic Solution to Some Double-Diffusive Convection System in the Whole Space Domain.** / Otani, Mitsuharu; Uchida, Shun.

Research output: Contribution to journal › Article

*Journal of Mathematical Fluid Mechanics*, vol. 20, no. 3, pp. 1035-1058. https://doi.org/10.1007/s00021-017-0354-1

}

TY - JOUR

T1 - Existence of Time Periodic Solution to Some Double-Diffusive Convection System in the Whole Space Domain

AU - Otani, Mitsuharu

AU - Uchida, Shun

PY - 2018/9/1

Y1 - 2018/9/1

N2 - This paper is concerned with the existence of time periodic solutions to some system which describes double-diffusive convection phenomena in the whole space RN 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.

AB - This paper is concerned with the existence of time periodic solutions to some system which describes double-diffusive convection phenomena in the whole space RN 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.

KW - Brinkman–Forchheimer equation

KW - Double-diffusive convection

KW - Large data

KW - Time periodic problem

KW - Whole space domain

UR - http://www.scopus.com/inward/record.url?scp=85051422415&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051422415&partnerID=8YFLogxK

U2 - 10.1007/s00021-017-0354-1

DO - 10.1007/s00021-017-0354-1

M3 - Article

AN - SCOPUS:85051422415

VL - 20

SP - 1035

EP - 1058

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 3

ER -