Abstract
This paper focuses on the inviscid limit of the incompressible Boussinesq equations in the same topology as the initial data, and proved that the continuous dependence of the viscous Boussinesq equations uniformly in some Besov spaces with respect to the viscosity. Our results extends the work of Guo et al. (J Funct Anal 276(9):2821–2830, 2019) on Navier–Stokes equations to Boussinesq equations with both stratified limit and earth’s rotation.
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The authors are very grateful to the anonymous reviewers for their careful read and useful suggestions, which greatly improved the presentation of the paper.
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Rong Chen is supported by Science and Technology Research Program of Chongqing Municipal Educational Commission (Grant No. KJQN202300544). Zhichun Yang is supported by the National Natural Science Foundation of China (No. 11971081). Shouming Zhou is partially supported by the National Natural Science Foundation of China (Grant No. 11971082), Science and Technology Research Program of Chongqing Municipal Educational Commission (Grant No.KJZD-M202200501).
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Chen, R., Yang, Z. & Zhou, S. The continuous dependence of the viscous Boussinesq equations uniformly with respect to the viscosity. Nonlinear Differ. Equ. Appl. 31, 14 (2024). https://doi.org/10.1007/s00030-023-00902-7
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DOI: https://doi.org/10.1007/s00030-023-00902-7