Under critical assumptions depending only on the horizontal angular component of the vorticity $w^{\theta }$ (whose detailed definition could be found in (1.3), (1.4) below), we prove that strong solutions of the viscid or inviscid MHD-Boussinesq systems, which are of zero magnetic resistivity, zero thermal diffusivity, and the magnetic field of which only has the horizontal angular component, can be smoothly extended beyond the possible blow-up time $T_{⁎}$. No a priori assumptions on the magnetic field or the temperature fluctuation are imposed.

中文翻译：

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w ^{θ 的}临界条件意味着轴对称 MHD-Boussinesq 系统的规律性

在仅取决于涡度的水平角分量的临界假设下 ${瓦}^{\theta }$ （其详细定义可在下面的（1.3）、（1.4）中找到），我们证明了粘性或无粘性 MHD-Boussinesq 系统的强解，它们具有零磁阻率、零热扩散率，并且其磁场仅具有水平角度分量，可平滑延长超出可能的爆破时间 ${吨}_{⁎}$. 没有强加对磁场或温度波动的先验假设。