On the local well-posedness and a Prodi–Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion
On the local well-posedness and a Prodi–Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion
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DOI：
10.1016/j.jde.2017.03.024
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发表时间：
2016-09
影响因子：
2.4
通讯作者：
Adam Larios;Yuan Pei
中科院分区：
文献类型：
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作者：
Adam Larios;Yuan Pei
本文证明了无热扩散的三维磁流体动力学Boussinesq系统（3DMHD-Boussinesq）的Prodi-Serrin型整体正则性条件，该条件只涉及两个速度和两个磁分量.据我们所知，这是第一个Prodi-Serrin型的标准，这样一个三维流体动力系统，这是不完全耗散，并表明，这种方法可能是成功的其他系统。此外，我们还对完全耗散的三维MHD-Boussinesq系统以及完全无粘、无阻、无扩散的MHD-Boussinesq方程的解的局部适定性提供了一个建设性的证明。我们注意到，作为特殊情况，这些结果包括三维非扩散Boussinesq系统和三维MHD方程。此外，它们可以毫无困难地扩展到包括科里奥利旋转项的情况。
We prove a Prodi–Serrin-type global regularity condition for the three-dimensional Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal diffusion, in terms of only two velocity and two magnetic components. To the best of our knowledge, this is the first Prodi–Serrin-type criterion for such a 3D hydrodynamic system which is not fully dissipative, and indicates that such an approach may be successful on other systems. In addition, we provide a constructive proof of the local well-posedness of solutions to the fully dissipative 3D MHD-Boussinesq system, and also the fully inviscid, irresistive, non-diffusive MHD-Boussinesq equations. We note that, as a special case, these results include the 3D non-diffusive Boussinesq system and the 3D MHD equations. Moreover, they can be extended without difficulty to include the case of a Coriolis rotational term.