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Global regularity results for the climate model with fractional dissipation

  • * Corresponding author: Jiahong Wu

    * Corresponding author: Jiahong Wu 
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.
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  • 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$.

    Mathematics Subject Classification: Primary: 35Q35, 35B65; Secondary: 76B03.


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