论文标题
三维非均匀性不可压缩热传导磁性水动力方程的强溶液
Strong Solutions for Three-dimensional Nonhomogeneous Incompressible Heat Conducting Magnetohydrodynamic Equations with Vacuum
论文作者
论文摘要
本文涉及整个空间中三维（3D）非均匀不可压缩的磁流体动力学（MHD）方程的库奇问题。首先，我们为强解决方案建立了弱的锯齿蛋白型爆炸标准。结果表明，对于3D非均匀热传导MHD方程的凯奇问题，如果速度满足弱锯齿蛋白的状况，则在全球存在强溶液。特别是，该标准与绝对温度和磁场无关。然后，作为立即应用，我们证明了在初始数据的某些较小条件下，对3D非均匀热传导MHD方程的强大解决方案的全球存在和独特性。另外，允许初始真空。
This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for the strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent of the absolute temperature and magnetic field. Then as an immediate application, we prove the global existence and uniqueness of strong solution to the 3D nonhomogeneous heat conducting MHD equations under some smallness condition on the initial data. In addition, the initial vacuum is allowed.
