Abstract
In this paper, we consider the global solutions to a generalized 2D Boussinesq equation
with \({\sigma \geq 0}\), \({\gamma \geq 0}\), \({\nu > 0}\), \({\kappa > 0}\), \({\alpha < 1}\) and \({\beta < 1}\). When \({\sigma = 0}\), \({\gamma \geq 0}\), \({\alpha \in [0.95,1)}\) and \({\beta \in (1-\alpha,g(\alpha))}\), where \({g(\alpha) < 1}\) is an explicit function as a technical bound, we prove that the above equation has a global and unique solution in suitable functional space.
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Jia, J., Peng, J. & Li, K. On the global well-posedness of a generalized 2D Boussinesq equations. Nonlinear Differ. Equ. Appl. 22, 911–945 (2015). https://doi.org/10.1007/s00030-014-0309-7
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DOI: https://doi.org/10.1007/s00030-014-0309-7