Application of the renormalization-group method to the reduction of transport equations
Application of the renormalization-group method to the reduction of transport equations
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DOI：
10.1088/0305-4470/39/25/s20
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发表时间：
2005-12
期刊：
影响因子：
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通讯作者：
T. Kunihiro;K. Tsumura
中科院分区：
文献类型：
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作者：
T. Kunihiro;K. Tsumura
我们首先全面回顾用于全局和渐进分析的重正化群方法，强调与经典包络理论的相关性以及所考虑的动力学不变流形存在的重要性。我们澄清该方法的一个要点是将问题从求解微分方程转换为获得合适的初始（或边界）条件：RG 方程确定了不变流形上的非微扰解中的潜在积分常数的慢运动。应用 RG 方法从玻尔兹曼方程导出纳维-斯托克斯方程，作为动力学简化的一个例子。我们研究如何根据单体分布函数获得传输系数。
We first give a comprehensive review of the renormalization-group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and on the importance of the existence of invariant manifolds of the dynamics under consideration. We clarify that an essential point of the method is to convert the problem from solving differential equations to obtaining suitable initial (or boundary) conditions: the RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. The RG method is applied to derive the Navier–Stokes equation from the Boltzmann equation, as an example of the reduction of dynamics. We work out how to obtain the transport coefficients in terms of the one-body distribution function.