Diffusive Limit of the Boltzmann Equation with Fluid Initial Layer in the Periodic Domain
Diffusive Limit of the Boltzmann Equation with Fluid Initial Layer in the Periodic Domain
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DOI：
10.1137/130922239
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发表时间：
2015-05
期刊：
影响因子：
--
通讯作者：
Ning Jiang;Linjie Xiong
中科院分区：
文献类型：
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作者：
Ning Jiang;Linjie Xiong
我们证明了周期域$\mathbb{T}^3 $内的玻尔兹曼方程的时间扩散极限。我们仅假设在初始膨胀$F^{\displaystyle $F ^{\mathrm}=\mu+\sqrt{\mu} f^{\mathrm}$ at $t=0$中，动力学部分是充分准备的，但流体部分可能是一般的，即，流体部分不需要满足不可压缩性和Boussinesq关系。对于这种情况，流体初始层被创建并保存在周期域中。利用时间平均的方法，分析了初始层的传播，推广了Guo在[Comm. Pure Appl. Math.，59（2006），pp. 626--687]，其中流体和动力部分都需要准备好。
We justify the global-in-time diffusive limit of the Boltzmann equation inside a periodic domain $\mathbb{T}^3$. We only assume that in the initial expansion $F^{\epsilon}=\mu+\sqrt{\mu} f^{\epsilon}$ at $t=0$, the kinetic parts are well-prepared, but the fluid parts could be general, i.e., the fluids parts are not required to satisfy the incompressibility and Boussinesq relations. For this case, the fluid initial layers are created and preserved in the periodic domain. Employing the method of time averaging, we analyze the propagation of the initial layers, and thus extend Guo's results in [Comm. Pure Appl. Math., 59 (2006), pp. 626--687] in which both fluid and kinetic parts are required to be well-prepared.