Generalization of some regularity criteria for 3D Boussinesq equations in homogeneous Besov and Triebel–Lizorkin spaces

References

[1] A. M. Alghamdi, S. Gala and M. A. Ragusa, A regularity criterion of weak solutions to the 3D Boussinesq equations, AIMS Math. 2 (2017), no. 3, 451–457. 10.3934/Math.2017.2.451Search in Google Scholar

[2] A. Barbagallo, S. Gala, M. A. Ragusa and M. Théra, On the regularity of weak solutions of the Boussinesq equations in Besov spaces, Vietnam J. Math. 49 (2021), no. 3, 637–649. 10.1007/s10013-020-00420-4Search in Google Scholar

[3] G. Bourdaud, Ce qu’il faut savoir sur les espaces de Besov, Preprint, Université Paris, 2009. Search in Google Scholar

[4] G. Bourdaud, M. Moussai and W. Sickel, Composition operators on Lizorkin–Triebel spaces, J. Funct. Anal. 259 (2010), no. 5, 1098–1128. 10.1016/j.jfa.2010.04.008Search in Google Scholar

[5] G. Bourdaud, M. Moussai and W. Sickel, Composition operators acting on Besov spaces on the real line, Ann. Mat. Pura Appl. (4) 193 (2014), no. 5, 1519–1554. 10.1007/s10231-013-0342-xSearch in Google Scholar

[6] J. Fan and T. Ozawa, Regularity criteria for the 3D density-dependent Boussinesq equations, Nonlinearity 22 (2009), no. 3, 553–568. 10.1088/0951-7715/22/3/003Search in Google Scholar

[7] S. Gala and M. A. Ragusa, A remark on the Beale–Kato–Majda criterion for the 3D MHD equations with zero magnetic diffusivity, AIP Conf. Proc. 1738 (2016), Article ID 480115. 10.1063/1.4952351Search in Google Scholar

[8] S. Gala and M. A. Ragusa, A regularity criterion of weak solutions to the 3D Boussinesq equations, Bull. Braz. Math. Soc. (N. S.) 51 (2020), no. 2, 513–525. 10.1007/s00574-019-00162-zSearch in Google Scholar

[9] J. Geng and J. Fan, A note on regularity criterion for the 3D Boussinesq system with zero thermal conductivity, Appl. Math. Lett. 25 (2012), no. 1, 63–66. 10.1016/j.aml.2011.07.008Search in Google Scholar

[10] N. Ishimura and H. Morimoto, Remarks on the blow-up criterion for the 3D-Boussinesq equations, Math. Models Methods Appl. Sci. 9 (1999), no. 9, 1323–1332. 10.1142/S0218202599000580Search in Google Scholar

[11] B. Jawerth, Some observations on Besov and Lizorkin–Triebel spaces, Math. Scand. 40 (1977), no. 1, 94–104. 10.7146/math.scand.a-11678Search in Google Scholar

[12] H. Kozono, T. Ogawa and Y. Taniuchi, The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations, Math. Z. 242 (2002), no. 2, 251–278. 10.1007/s002090100332Search in Google Scholar

[13] A. Majda, Introduction to PDEs and Waves for the Atmosphere and Ocean, Courant Lect. Notes Math. 9, New York University, New York, 2003. 10.1090/cln/009Search in Google Scholar

[14] M. Moussai, Realizations of homogeneous Besov and Triebel–Lizorkin spaces and an application to pointwise multipliers, Anal. Appl. (Singap.) 13 (2015), no. 2, 149–183. 10.1142/S0219530514500250Search in Google Scholar

[15] T. T. Ngoc and P. T. Xuan, On pseudo almost periodic solutions for Boussinesq systems on real hyperbolic manifolds, Filomat 39 (2025), no. 6, 1883–1894. 10.2298/FIL2506883NSearch in Google Scholar

[16] Y. Pandir and Y. Gurefe, A new version of the generalized F-expansion method for the fractional Biswas–Arshed equation and Boussinesq equation with the beta-derivative, J. Funct. Spaces 2023 (2023), Article ID 1980382. 10.1155/2023/1980382Search in Google Scholar

[17] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. 1, Duke University, Durham, 1976. Search in Google Scholar

[18] H. Qiu, Y. Du and Z. Yao, Blow-up criteria for 3D Boussinesq equations in the multiplier space, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 4, 1820–1824. 10.1016/j.cnsns.2010.08.036Search in Google Scholar

[19] E. A. Spiegel and G. Veronis, On the Boussinesq approximation for a compressible fluid, Astrophys. J. 131 (1960), 442–447. 10.1086/146849Search in Google Scholar

[20] H. Triebel, Theory of Function Spaces, Monogr. Math. 78, Birkhäuser, Basel, 1983. 10.1007/978-3-0346-0416-1Search in Google Scholar

[21] Z. Ye, Regularity criteria for 3D Boussinesq equations with zero thermal diffusion, Electron. J. Differential Equations 2015 (2015), no. 97, 1–7. Search in Google Scholar

[22] Z. Zhang, Some regularity criteria for the 3D Boussinesq equations in the class L 2 ⁢ ( 0 , T ; B ˙ ∞ , ∞ - 1 ) , ISRN Appl. Math. 2014 (2014), Article ID 564758. 10.1155/2014/564758Search in Google Scholar