## Osaka Journal of Mathematics

- Osaka J. Math.
- Volume 53, Number 3 (2016), 855-872.

### Global solvability for double-diffusive convection system based on Brinkman--Forchheimer equation in general domains

Mitsuharu Ôtani and Shun Uchida

#### Abstract

In this paper, we are concerned with the solvability of the initial boundary value problem of a system which describes double-diffusive convection phenomena in some porous medium under general domains, especially unbounded domains. In previous works where the boundedness of the space domain is imposed, some global solvability results have been already derived. However, when we consider our problem in general domains, some compactness theorems are not available. Hence it becomes difficult to follow the same strategies as before. Nevertheless, we can assure the global existence of a unique solution via the contraction method. Moreover, it is revealed that the global solvability holds for higher space dimension and larger class of the initial data than those assumed in previous works.

#### Article information

**Source**

Osaka J. Math., Volume 53, Number 3 (2016), 855-872.

**Dates**

First available in Project Euclid: 5 August 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ojm/1470413994

**Mathematical Reviews number (MathSciNet)**

MR3533473

**Zentralblatt MATH identifier**

1365.35057

**Subjects**

Primary: 35K45: Initial value problems for second-order parabolic systems

Secondary: 35Q35: PDEs in connection with fluid mechanics 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]

#### Citation

Ôtani, Mitsuharu; Uchida, Shun. Global solvability for double-diffusive convection system based on Brinkman--Forchheimer equation in general domains. Osaka J. Math. 53 (2016), no. 3, 855--872. https://projecteuclid.org/euclid.ojm/1470413994