Global regularity for the 3D MHD system with\nobreakspace {}damping
Volume 145 / 2016
Colloquium Mathematicum 145 (2016), 107-110
MSC: Primary 35Q35; Secondary 35B35, 35B65, 76D03.
DOI: 10.4064/cm6654-9-2015
Published online: 22 April 2016
Abstract
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.
