# American Institute of Mathematical Sciences

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January  2019, 24(1): 211-229. doi: 10.3934/dcdsb.2018102

## Global regularity results for the climate model with fractional dissipation

 1 School of Mathematical Sciences, Anhui University, Hefei 230601, China 2 Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA 3 School of Mathematics and computation Sciences, Anqing Normal University, Anqing 246133, China

* Corresponding author: Jiahong Wu

Received  January 2017 Revised  January 2018 Published  January 2019 Early access  March 2018

Fund Project: B. Dong was partially supported by the NNSFC (No. 11271019, No. 11571240). J. Wu was supported by NSF grant DMS 1614246 and the AT & T Foundation at Oklahoma State University. H. Zhang was as partially supported by the Research Fund of SMS at Anhui University.

This paper studies the global well-posedness problem on a tropical climate model with fractional dissipation. This system allows us to simultaneously examine a family of equations characterized by the fractional dissipative terms $(-Δ)^{\mathit{\alpha }}u$ in the equation of the barotropic mode $u$ and $(-Δ)^β v$ in the equation of the first baroclinic mode $v$. We establish the global existence and regularity of the solutions when the total fractional power is 2, namely ${\mathit{\alpha }}+ β = 2$.

Citation: Boqing Dong, Wenjuan Wang, Jiahong Wu, Hui Zhang. Global regularity results for the climate model with fractional dissipation. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 211-229. doi: 10.3934/dcdsb.2018102
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