194 research outputs found
The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations
We study the blow-up criterion of smooth solutions to the 3D MHD equations.
By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda
type blow-up criterion of smooth solutions via the vorticity of velocity only,
i. e. \sup_{j\in\Z}\int_0^T\|\Delta_j(\na\times u)\|_\infty dt, where
is a frequency localization on .Comment: 12page
On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces
In this paper, we prove the local well-posedness for the Ideal MHD equations
in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth
solutions. Specially, we fill a gap in a step of the proof of the local
well-posedness part for the incompressible Euler equation in \cite{Chae1}.Comment: 16page
Existence theorem and blow-up criterion of the strong solutions to the Magneto-micropolar fluid equations
In this paper we study the magneto-micropolar fluid equations in ,
prove the existence of the strong solution with initial data in for
, and set up its blow-up criterion. The tool we mainly use is
Littlewood-Paley decomposition, by which we obtain a Beale-Kato-Majda type
blow-up criterion for smooth solution which relies on the
vorticity of velocity only.Comment: 19page
Existence theorem and blow-up criterion of strong solutions to the two-fluid MHD equation in
We first give the local well-posedness of strong solutions to the Cauchy
problem of the 3D two-fluid MHD equations, then study the blow-up criterion of
the strong solutions. By means of the Fourier frequency localization and Bony's
paraproduct decomposition, it is proved that strong solution can be
extended after if either with
and , or
with , where \omega(t)=\na\times u denotes the vorticity of the velocity and
J=\na\times b the current density.Comment: 18 page
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