Global well-posedness of strong solutions to the 2D damped Boussinesq and MHD equations with large velocity

In this paper, we obtain global well-posedness for the 2D damped Boussinesq equations. Based on the estimate of the damped Euler equations leading to the uniform corresponding bound which does not grow in time, we can achieve this goal by using a new decomposition technique. Comparing with the previous works [D. Adhikar, C. Cao, J. Wu, and X. Xu, J. Diff. Eqs., 256:3594–3613, 2014] and [J. Wu, X. Xu, and Z. Ye, J. Nonlineal Sci., 25:157–192, 2015], we do not need any small assumptions of the initial velocity. As an application of our method, we obtain a similar result for the 2D damped MHD equations.

Keywords

Boussinesq equations, MHD equations, global well-posedness

2010 Mathematics Subject Classification

35Q35, 76B03

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Received 9 August 2016

Published 27 June 2017