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

Mitsuharu Otani; Shun Uchida

doi:10.1007/s00021-017-0354-1

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

Mitsuharu Otani, Shun Uchida^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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	https://doi.org/10.1007/s00021-017-0354-1
Publication status	Published - 2018 Sept 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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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 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.",

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

author = "Mitsuharu Otani and Shun Uchida",

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AU - Otani, Mitsuharu

AU - Uchida, Shun

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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

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

Abstract

Keywords

ASJC Scopus subject areas

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