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Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations

Published online by Cambridge University Press:  22 January 2016

Dongho Chae ,
Sung-Ki Kim  and
Hee-Seok Nam
Dongho Chae
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea, dhchae@math.snu.ac.kr
Sung-Ki Kim
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea, skkim@math.snu.ac.kr
Hee-Seok Nam
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea, heedol@math.snu.ac.kr
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Abstract

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In this paper we prove the local existence and uniqueness of C1+γ solutions of the Boussinesq equations with initial data υ0, θ0 ∈ C1+γ, ω0, ∇θ0 ∈ Lq for 0 < γ < 1 and 1 < q < 2. We also obtain a blow-up criterion for this local solutions. More precisely we show that the gradient of the passive scalar θ controls the breakdown of C1+γ solutions of the Boussinesq equations.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 155 , 1999 , pp. 55 - 80
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

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