Abstract
In the present paper, we consider the Cauchy problem of nonhomogeneous heat conducting Navier–Stokes equations in the whole space \({\mathbb {R}}^2\). Combining delicate energy estimates and a logarithmic interpolation inequality, we derive the global existence and uniqueness of strong solutions. In particular, the initial data can be arbitrarily large.
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Acknowledgements
The author would like to express his gratitude to the reviewers for careful reading and helpful suggestions which led to an improvement of the original manuscript.
Funding
This research was partially supported by National Natural Science Foundation of China (Nos. 11901474, 12071359) and Exceptional Young Talents Project of Chongqing Talent (No. cstc2021ycjh-bgzxm0153).
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Zhong, X. Global Well-Posedness to the Cauchy Problem of Two-Dimensional Nonhomogeneous Heat Conducting Navier-Stokes Equations. J Geom Anal 32, 200 (2022). https://doi.org/10.1007/s12220-022-00947-7
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DOI: https://doi.org/10.1007/s12220-022-00947-7