Global Well-Posedness for Euler–Boussinesq System with Critical Dissipation

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On the global well-posedness of a class of Boussinesq–Navier–Stokes systems (2009, methodology): “For = 1, β = 1 and f = 0, the result has appeared in [11].”
On a maximum principle and its application to logarithmically critical Boussinesq system (2009, background): “The proof shares the same ideas as the case α = 0 treated in [15] but with more technical difficulties.”
Global Regularity for Some Oldroyd‐B Type Models (2013, methodology): “We refer to the book [1] or the introduction of [12] for the definition of Besov spaces.”
Global regularity for the 2D anisotropic Boussinesq Equations with vertical dissipation (2011, background): “Further progress on these two cases was recently made by Hmidi, Keraani and Rousset, who were able to establish the global regularity even when the full Laplacian dissipation is replaced by the critical dissipation represented in terms of the operator √ −∆ ([17],[18]).”
Global Regularity for a Class of Generalized Magnetohydrodynamic Equations (2011, background): “Remark. The special case in (2.4) has previously been obtained by Hmidi et al. [ 12 ].”
Nonlinear maximum principles for dissipative linear nonlocal operators and applications (2011, background): “The well-posedness of (B0,2) and (B2,0) have been obtained in [5, 19], while the scaling critical cases (B1,0) and (B0,1) have been resolved in [20] and [21] respectively.”