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

Authors
Chae, D Kim, SK Nam, HS
Citation
D. Chae et al., Local existence and blow-up criterion of Holder continuous solutions of the Boussinesq equations, NAG MATH J, 155, 1999, pp. 55-80
Citations number
7
Categorie Soggetti
Mathematics
Journal title
NAGOYA MATHEMATICAL JOURNAL
ISSN journal
00277630 → ACNP
Volume
155
Year of publication
1999
Pages
55 - 80
Database
ISI
SICI code
0027-7630(199909)155:<55:LEABCO>2.0.ZU;2-W
Abstract
In this paper we prove the local existence and uniqueness of C1+gamma solut ions of the Boussinesq equations with initial data v(0), theta(0) epsilon C 1+gamma, w(0), del theta(0) epsilon L-q for 0 < gamma < 1 and 1 < q < 2. We also obtain a blow-up criterion for this local solutions. More precisely w e show that the gradient of the passive scalar theta controls the breakdown of C1+gamma solutions of the Boussinesq equations.