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The weak sigma-attractor for the semi-dissipative 2D Boussinesq system


Authors: Jinfang He and Chunyou Sun
Journal: Proc. Amer. Math. Soc. 148 (2020), 1219-1231
MSC (2010): Primary 35B41, 35Q35, 76D09, 76F25
DOI: https://doi.org/10.1090/proc/14807
Published electronically: November 4, 2019
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Abstract: In this paper, we obtain the attraction properties for the velocity variable of the 2D Boussinesq equations with viscosity and without heat diffusion in the sense of the strong topology of $ V$ and prove that the weak sigma-attractor has a pancake-like structure, which answer partly some questions arising in Biswas et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), pp. 381-405] and enrich the structure of the weak sigma-attractor.


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Additional Information

Jinfang He
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China
Email: hejf14@lzu.edu.cn

Chunyou Sun
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China
Email: sunchy@lzu.edu.cn

DOI: https://doi.org/10.1090/proc/14807
Keywords: Weak sigma-attractor, Boussinesq equations, semi-dissipative system
Received by editor(s): April 10, 2019
Received by editor(s) in revised form: July 24, 2019
Published electronically: November 4, 2019
Additional Notes: This work was supported by the NSFC (Grants No. 11471148, 11522109 and 11871169)
The second author is the corresponding author
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society