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Global regularity for the 3D MHD system with\nobreakspace {}damping

Volume 145 / 2016

Zujin Zhang, Xian Yang Colloquium Mathematicum 145 (2016), 107-110 MSC: Primary 35Q35; Secondary 35B35, 35B65, 76D03. DOI: 10.4064/cm6654-9-2015 Published online: 22 April 2016


We study the Cauchy problem for the 3D MHD system with damping terms $\varepsilon |\boldsymbol {u}|^{\alpha -1}\boldsymbol {u}$ and $\delta |\boldsymbol {b}|^{\beta -1}\boldsymbol {b}$ ($\varepsilon ,\delta \gt 0$ and $\alpha ,\beta \geq 1$), and show that the strong solution exists globally for any $\alpha ,\beta \gt 3$. This improves the previous results significantly.


  • Zujin ZhangSchool of Mathematics and Computer Science
    Gannan Normal University
    Ganzhou 341000, Jiangxi, P.R. China
  • Xian YangForeign Languages Department
    Ganzhou Teachers College
    Ganzhou 341000, Jiangxi, P.R. China

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