Ye, Zhuan An alternative approach to global regularity for the 2D Euler-Boussinesq equations with critical dissipation. (English) Zbl 1431.35142 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 190, Article ID 111591, 5 p. (2020). Summary: The purpose of this paper is to provide an alternative approach to the global regularity for the two-dimensional Euler-Boussinesq equations which couple the incompressible Euler equation for the velocity and a transport equation with fractional critical diffusion for the temperature. In contrast to the first proof of this result in [T. Hmidi et al., Commun. Partial Differ. Equations 36, No. 1–3, 420–445 (2011; Zbl 1284.76089)] that took fully exploit of the hidden structure of the coupling system, the main argument in this manuscript is mainly based on the differentiability of the drift-diffusion equation. MSC: 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 35R11 Fractional partial differential equations Keywords:Boussinesq equations; global regularity PDF BibTeX XML Cite \textit{Z. Ye}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 190, Article ID 111591, 5 p. (2020; Zbl 1431.35142) Full Text: DOI References: [1] Bahouri, H.; Chemin, J.-Y.; Danchin, R., Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren Der Mathematischen Wissenschaften, 343 (2011), Springer [2] Brezis, H.; Wainger, S., A note on limiting cases of Sobolev embedding and convolution inequalities, Comm. Partial Differential Equations, 5, 773-789 (1980) · Zbl 0437.35071 [3] Hmidi, T.; Keraani, S.; Rousset, F., Global well-posedness for Euler-Boussinesq system with critical dissipation, Comm. Partial Differential Equations, 36, 420-445 (2011) · Zbl 1284.76089 [4] Kato, T.; Ponce, G., Commutator estimates and the Euler and the Navier-Stokes equations, Comm. Pure Appl. Math., 41, 891-907 (1988) · Zbl 0671.35066 [5] Majda, A.; Bertozzi, A., Vorticity and Incompressible Flow (2001), Cambridge University Press: Cambridge University Press Cambridge [6] Pedlosky, J., Geophysical Fluid Dynamics (1987), Springer-Verlag: Springer-Verlag New York · Zbl 0713.76005 [7] Silvestre, L., On the differentiablity of the solution to an equation with drift and fractional diffusion, Indiana Univ. Math. J., 61, 2, 557-584 (2012) · Zbl 1308.35042 [8] Xue, L.; Ye, Z., On the differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion, Pacific J. Math., 293, 471-510 (2018) · Zbl 1379.35049 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.