Global Well-Posedness of 3D Axisymmetric MHD System with Pure Swirl Magnetic Field
Tóm tắt
In this paper, we consider the axisymmetric MHD system with nearly critical initial data having the special structure:
$u_{0}=u_{0}^{r} e_{r}+u^{\theta}_{0} e_{\theta}+u_{0}^{z} e_{z}$
,
$b_{0}=b_{0}^{\theta}e_{\theta}$
. We prove that, this system is globally well-posed provided the scaling-invariant norms
$\|ru^{\theta}_{0}\|_{L^{\infty}}$
,
$\|r^{-1}b^{\theta}_{0}\| _{L^{\frac{3}{2}}}$
are sufficiently small.
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