### Abstract

We study weak solutions of the initial and boundary value problems of the Boussinesq equations which describe the natural convection in a viscous incompressible fluid. We construct a global weak solution for the initial velocity in L^{2} and the initial temperature in L^{1}. We show that the temperature θ(x, t) of our weak solution is Hölder continuous in x for almost every t > 0. In general, it is not known whether weak solutions are unique or not. We show that weak solutions are unique if they are in some Lebesgue space. We show, moreover, that weak solutions are regular if they belong to the uniqueness class.

Original language | English |
---|---|

Pages (from-to) | 587-611 |

Number of pages | 25 |

Journal | Differential and Integral Equations |

Volume | 6 |

Issue number | 3 |

Publication status | Published - 1993 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Differential and Integral Equations*,

*6*(3), 587-611.

**On weak solutions of nonstationary boussinesq equations.** / Kagei, Yoshiyuki.

Research output: Contribution to journal › Article

*Differential and Integral Equations*, vol. 6, no. 3, pp. 587-611.

}

TY - JOUR

T1 - On weak solutions of nonstationary boussinesq equations

AU - Kagei, Yoshiyuki

PY - 1993

Y1 - 1993

N2 - We study weak solutions of the initial and boundary value problems of the Boussinesq equations which describe the natural convection in a viscous incompressible fluid. We construct a global weak solution for the initial velocity in L2 and the initial temperature in L1. We show that the temperature θ(x, t) of our weak solution is Hölder continuous in x for almost every t > 0. In general, it is not known whether weak solutions are unique or not. We show that weak solutions are unique if they are in some Lebesgue space. We show, moreover, that weak solutions are regular if they belong to the uniqueness class.

AB - We study weak solutions of the initial and boundary value problems of the Boussinesq equations which describe the natural convection in a viscous incompressible fluid. We construct a global weak solution for the initial velocity in L2 and the initial temperature in L1. We show that the temperature θ(x, t) of our weak solution is Hölder continuous in x for almost every t > 0. In general, it is not known whether weak solutions are unique or not. We show that weak solutions are unique if they are in some Lebesgue space. We show, moreover, that weak solutions are regular if they belong to the uniqueness class.

UR - http://www.scopus.com/inward/record.url?scp=84972500181&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972500181&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972500181

VL - 6

SP - 587

EP - 611

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 3

ER -