高斯非相对论自发随机流体动力学
Gaussian non relativistic spontaneously stochastic hydrodynamics
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中文总结 AI 辅助
该研究推导高斯协变流体动力学非相对论极限的重整化群方程，揭示微观尺度下不可压缩性失效，自发随机性为统计涨落的宏观反作用，为湍流数学问题提供物理视角。
中文摘要 AI 辅助
我们研究高斯协变流体动力学的非相对论极限[1]。我们认为不可压缩性条件提供了与相对论流体动力学匹配的额外对称性，但不可压缩性必须在“微观”尺度上失效。随后，我们针对平均量和涨落量相对于该尺度推导了重整化群方程，以理解其对分子间距离处流动的影响——在该尺度上流体动力学让位于统计力学。所得动力学自然将自发随机性纳入其中，作为统计力学涨落的宏观反作用，还包含类似反常耗散和“狂野解”的特征，作为重整化群抵消项。我们将这些考虑纳入流体动力学适用范围的唯象讨论，以及物理学可能为湍流相关数学问题提供启示的讨论中。
英文摘要
We study the non-relativistic limit of Gaussian covariant hydrodynamics [1]. We argue that the condition of incompressibility provides additional symmetries matching relativistic hydrodynamics but incompressibility must break down at a ``microscopic`` scale. We then develop the renormalization group equations for average and fluctuations w.r.t. that scale, to understand its effect on flows at intermolecular distances where hydrodynamics gives way to statistical mechanics. The resulting dynamics naturally incorporates spontaneous stochasticity as a macroscopic back reaction of statistical mechanics fluctuations, as well as features reminiscent of anomalous dissipation and ``wild solutions`` as renormalization group counterterms. We frame these considerations into both a phenomenological discussion of the limits of applicability of fluid dynamics, and a discussion of where physics might shed some light on the mathematical issues associated with turbulence.
