Serrin-Type Blowup Criterion for Viscous,Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows
Serrin-Type Blowup Criterion for Viscous,Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows
复制标题
粘性、可压缩、导热纳维斯托克斯和磁流体动力流的 Serrin 型吹胀准则
DOI：
10.1007/s00220-013-1791-1
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发表时间：
2013
影响因子：
2.4
通讯作者：
Jing Li
中科院分区：
文献类型：
--
作者：
Xiangdi Huang;Jing Li
建立了三维粘性、可压缩、导热磁流体流动的爆破准则。结果表明，对于三维可压缩MHD流的Cauchy问题和初边值问题，当初始密度为零时，当密度有界且速度满足Serrin条件时，强解或光滑解整体存在.因此，如果速度的Serrin范数保持有界，则在密度变为无界之前，不可能形成其他类型的奇点（例如真空态消失或在非真空区域出现真空或更温和的奇点）。该判据类似于三维不可压Navier-Stokes方程的Serrin爆破判据，特别是与温度和磁场无关，与正压可压Navier-Stokes方程的爆破判据相同。作为一个直接的应用程序，它表明，同样的结果也适用于强或光滑的解决方案，三维完全可压缩的Navier-Stokes系统描述的粘性，可压缩，导热流体的运动。
This paper establishes a blowup criterion for the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic (MHD) flows. It is essentially shown that for the Cauchy problem and the initial-boundary-value one of the three-dimensional compressible MHD flows with initial density allowed to vanish, the strong or smooth solution exists globally if the density is bounded from above and the velocity satisfies Serrin’s condition. Therefore, if the Serrin norm of the velocity remains bounded, it is not possible for other kinds of singularities (such as vacuum states vanishing or vacuum appearing in the non-vacuum region or even milder singularities) to form before the density becomes unbounded. This criterion is analogous to the well-known Serrin’s blowup criterion for the three-dimensional incompressible Navier-Stokes equations, in particular, it is independent of the temperature and magnetic field and is just the same as that of the barotropic compressible Navier-Stokes equations. As a direct application, it is shown that the same result also holds for the strong or smooth solutions to the three-dimensional full compressible Navier-Stokes system describing the motion of a viscous, compressible, and heat conducting fluid.