zbMATH — the first resource for mathematics

Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations. (English) Zbl 0939.35150
The authors consider the initial-boundary value problem for a system of equations which models the interactive motion of a passive scalar (e.g. temperature) in atmosphere with an external potential force (a modification of Boussinesq equations). The problem is reduced to an equivalent integro-differential equation for particle trajectories of the flow, and then the application of Picard-type iterations and Lipschitz estimates in an appropriate Banach space provides the existence and uniqueness of a local solution. Finally, in terms of the gradient of the passive scalar, the authors establish a blow-up criterion in Hölder space for this local solution.
Reviewer: O.Titow (Berlin)

35Q35 PDEs in connection with fluid mechanics
76R99 Diffusion and convection
86A10 Meteorology and atmospheric physics
Full Text: DOI
[1] Nonlinearity and functional analysis (1977)
[2] DOI: 10.1007/BF01212349 · Zbl 0573.76029 · doi:10.1007/BF01212349
[3] J. Math. Pures Appl. 73 pp 335– (1994)
[4] DOI: 10.1017/S0308210500026810 · Zbl 0882.35096 · doi:10.1017/S0308210500026810
[5] pp 1– · Zbl 0239.13011
[6] J. Math. Pures Appl. 71 pp 407– (1992)
[7] Vorticity and the mathematical theory of incompressible fluid flow pp 1986–
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.