Pointwise space–time estimates of non-isentropic compressible micropolar fluids
Pointwise space–time estimates of non-isentropic compressible micropolar fluids
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DOI：
10.1007/s00033-021-01468-z
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发表时间：
2021-04
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影响因子：
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通讯作者：
Zhigang Wu;Xiaopan Jiang
中科院分区：
文献类型：
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作者：
Zhigang Wu;Xiaopan Jiang
对于三维非等熵可压缩微极性流体，我们发现流体密度、动量和能量的时空行为同时包含广义惠更斯波和扩散波作为非等熵可压缩纳维-斯托克斯方程，而对于微观有理速度只包含扩散波。之前所有包含惠更斯波的可压缩流模型波动行为的估计都严重依赖于保守结构，例如等熵和非等熵纳维-斯托克斯方程。本文利用流体和电磁部分的分解方法研究了三个较小的格林矩阵，发现其中一个矩阵类似于非等熵纳维-斯托克斯方程，但由于微有理速度的存在，其能量不再保守。我们通过为格林矩阵提供精确的估计来克服这个困难。另一个困难是证明微有理速度的逐点估计仅包含扩散波，尽管其非线性项包含惠更斯波和扩散波。它是通过利用这两个波的关系并开发新的非线性估计来解决的。我们的逐点估计直接产生yield-estimate，这是通常估计的概括。
For the non-isentropic compressible micropolar fluids in three dimensions, we show that the space–time behaviors of the fluid density, momentum and energy contain both generalized Huygens’ wave and diffusion wave as the non-isentropic compressible Navier–Stokes equation, while it only contains the diffusion wave for the micro-rational velocity. All of the previous estimates containing Huygens’ waves for wave behaviors of compressible flow models rely heavily on the conservative structure, for instance, the isentropic and non-isentropic Navier–Stokes equations. In this paper, after using the decomposition of fluid and electromagnetic parts to study three smaller Green’s matrices, we find that one of them is like a non-isentropic Navier–Stokes equation, but its energy is not conservative anymore due to the presence of the micro-rational velocity. We overcome this difficulty by providing a refined estimate for this Green’s matrix. Another difficulty is in proving the pointwise estimate of the micro-rational velocity only contains the diffusion wave, although its nonlinear terms contain both the Huygens’ wave and the diffusion wave. It is solved by using the relation of these two waves and developing new nonlinear estimates. Our pointwise estimate directly yields-estimate with, which is a generalization of the usual-estimate.