Higher Order Regularity and Blow-up Criterion for Semi-dissipative and Ideal Boussinesq Equations

In this paper we establish local-in-time existence and uniqueness of strong solutions in \(H^s\) for \(s > \frac{n}{2}\) to the viscous, zero thermal-diffusive Boussinesq equations in \(\mathbb{R}^n , n = 2,3\). Beale-Kato-Majda type blow-up criterion has been established in three-dimensions with...

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Bibliographic Details
Published in:arXiv.org 2017-06
Main Authors: Manna, Utpal, Panda, Akash A
Format: Article
Language:English
Subjects:
Boussinesq equations
Commutators
Criteria
Mathematical analysis
Vorticity
Online Access:Get full text
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Summary:In this paper we establish local-in-time existence and uniqueness of strong solutions in \(H^s\) for \(s > \frac{n}{2}\) to the viscous, zero thermal-diffusive Boussinesq equations in \(\mathbb{R}^n , n = 2,3\). Beale-Kato-Majda type blow-up criterion has been established in three-dimensions with respect to the \(BMO\)-norm of the vorticity. We further prove the local-in-time existence and blow-up criterion for non-viscous and fully ideal Boussinesq systems. Commutator estimates due to Kato and Ponce (1988) \cite {KP} and Fefferman et. al. (2014) \cite {Fe} play important roles in the calculations.
ISSN:2331-8422