Translator Disclaimer
1999 Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
Dongho Chae, Sung-Ki Kim, Hee-Seok Nam
Nagoya Math. J. 155: 55-80 (1999).

Abstract

In this paper we prove the local existence and uniqueness of $C^{1+\gamma}$ solutions of the Boussinesq equations with initial data $v_0$, $\theta_0 \in C^{1+\gamma}$, $\omega_0, \Delta\theta_0\in L^q$ for $0 < \gamma < 1$ 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 $\theta$ controls the breakdown of $C^{1+\gamma}$ solutions of the Boussinesq equations.

Citation

Download Citation

Dongho Chae. Sung-Ki Kim. Hee-Seok Nam. "Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations." Nagoya Math. J. 155 55 - 80, 1999.

Information

Published: 1999
First available in Project Euclid: 27 April 2005

zbMATH: 0939.35150
MathSciNet: MR1711383

Subjects:
Primary: 35Q35
Secondary: 35B05, 76B03

Rights: Copyright © 1999 Editorial Board, Nagoya Mathematical Journal

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.155 • 1999
Back to Top