The Asymptotic Stability of the Solution to the Full Hall-MHD System in \(\mathbb {R}^3\)

  • Leilei TongEmail author
  • Zhong Tan


In this paper, we consider the asymptotic stability of the solutions near a constant equilibrium state to the Cauchy problem for the compressible full Hall-MHD equations in \(\mathbb {R}^3\). We employ the energy estimate and introduce the negative Sobolev and Besov spaces to get the global existence and decay rates of the solution under the assumption that the \(H^3\) norm of the initial perturbation is small. As an immediate byproduct, the \(L^p-L^2\)\((1\leqslant p\leqslant 2)\) type of the decay rates follows without requiring the smallness for \(L^p\) norm of initial data.


Full Hall-MHD equations Optimal decay rates Energy method Regular interpolation 

Mathematics Subject Classification

76W05 35Q35 35B40 



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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsChongqing University of Posts and TelecommunicationsChongqingPeople’s Republic of China
  2. 2.School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific ComputingXiamen UniversityXiamenPeople’s Republic of China

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