### Abstract

We prove the existence of a strong-weak solution (u,p,T) (= velocity, pressure, temperature) of the steady Bénard problem in a 2D quadrangular cavity, heated/cooled on two opposite sides and thermally insulated on the other sides. Applying the tools of nonlinear analysis, we study the structure of the set of solutions in dependence on the acting volume force and on the given temperature profiles on the heated/cooled sides. Particularly, in the case when the cavity has the form of a trapezoid, we also study the structure of the solution set in dependence on the angle of inclination from the horizontal-vertical position.

Original language | English |
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Pages (from-to) | 68-88 |

Number of pages | 21 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 123-124 |

DOIs | |

Publication status | Published - May 19 2015 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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**Existence and structure of steady solutions of the Bénard problem in a two dimensional quadrangular cavity.** / Neustupa, Jiří; Siginer, Dennis.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Existence and structure of steady solutions of the Bénard problem in a two dimensional quadrangular cavity

AU - Neustupa, Jiří

AU - Siginer, Dennis

PY - 2015/5/19

Y1 - 2015/5/19

N2 - We prove the existence of a strong-weak solution (u,p,T) (= velocity, pressure, temperature) of the steady Bénard problem in a 2D quadrangular cavity, heated/cooled on two opposite sides and thermally insulated on the other sides. Applying the tools of nonlinear analysis, we study the structure of the set of solutions in dependence on the acting volume force and on the given temperature profiles on the heated/cooled sides. Particularly, in the case when the cavity has the form of a trapezoid, we also study the structure of the solution set in dependence on the angle of inclination from the horizontal-vertical position.

AB - We prove the existence of a strong-weak solution (u,p,T) (= velocity, pressure, temperature) of the steady Bénard problem in a 2D quadrangular cavity, heated/cooled on two opposite sides and thermally insulated on the other sides. Applying the tools of nonlinear analysis, we study the structure of the set of solutions in dependence on the acting volume force and on the given temperature profiles on the heated/cooled sides. Particularly, in the case when the cavity has the form of a trapezoid, we also study the structure of the solution set in dependence on the angle of inclination from the horizontal-vertical position.

UR - http://www.scopus.com/inward/record.url?scp=84929379089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929379089&partnerID=8YFLogxK

U2 - 10.1016/j.na.2015.03.024

DO - 10.1016/j.na.2015.03.024

M3 - Article

AN - SCOPUS:84929379089

VL - 123-124

SP - 68

EP - 88

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -