In this paper, we investigate the Cauchy problem for the 3D incompressible Hall-MHD equations with zero viscosity. We prove the Beale-Kato-Majda regularity criterion of smooth solutions in terms of the velocity field and magnetic field in the homogeneous Besov spaces $dot{B}_{infty ,infty }^{0} $. Then we give a criterion on extension beyond $T$ of our local solution. Our result may be also regarded as an extension of the corresponding result of cite{WZuo}.
Beale-Kato-Majda regularity criterion of smooth solutions for the Hall-MHD equations with zero viscosity
Maria Alessandra Ragusa
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2022-01-01
Abstract
In this paper, we investigate the Cauchy problem for the 3D incompressible Hall-MHD equations with zero viscosity. We prove the Beale-Kato-Majda regularity criterion of smooth solutions in terms of the velocity field and magnetic field in the homogeneous Besov spaces $dot{B}_{infty ,infty }^{0} $. Then we give a criterion on extension beyond $T$ of our local solution. Our result may be also regarded as an extension of the corresponding result of cite{WZuo}.File in questo prodotto:
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