News & Announcements
Links
Local Existence of Strong Solutions to the Generalized MHD Equations
  
View Full Text  View/Add Comment  Download reader
KeyWord:Generalized MHD system, local existence, Fourier truncation
Author NameAffiliation
Liangbing Jin School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Xinru Cheng School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Hits: 49
Download times: 47
Abstract:
      This paper devotes to consider the local existence of the strong solutions to the generalized MHD system with fractional dissipative terms $\Lambda^{2\alpha}u$ for the velocity field and $\Lambda^{2\alpha}b$ for the magnetic field, respectively. We construct the approximate solutions by the Fourier truncation method, and use energy method to obtain the local existence of strong solutions in $H^s(\mathbb{R}^n)\,(s>\max \left\{\frac{n}{2}+1-2\alpha, 0\right\})$ for any $\alpha\geq0$.