Carrillo José Antonio, Chen Xiuqing, Du Bang, Jüngel Ansgar
Mathematical Institute, University of Oxford, Oxford, OX2 66G UK.
School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082 Guangdong Province China.
Commun Math Phys. 2025;406(7):151. doi: 10.1007/s00220-025-05341-2. Epub 2025 Jun 3.
The Busenberg-Travis cross-diffusion system for segregating populations is approximated by the compressible Navier-Stokes-Korteweg equations on the torus, including a density-dependent viscosity and drag forces. The Korteweg term can be associated to the quantum Bohm potential. The singular asymptotic limit is proved rigorously using compactness and relative entropy methods. The novelty is the derivation of energy and entropy inequalities, which reduce in the asymptotic limit to the Boltzmann-Shannon and Rao entropy inequalities, thus revealing the double entropy structure of the limiting Busenberg-Travis system.
用于隔离种群的布森伯格 - 特拉维斯交叉扩散系统由环面上的可压缩纳维 - 斯托克斯 - 科特韦格方程近似表示，其中包括密度依赖的粘性和阻力。科特韦格项可以与量子玻姆势相关联。利用紧致性和相对熵方法严格证明了奇异渐近极限。新颖之处在于能量和熵不等式的推导，在渐近极限中它们简化为玻尔兹曼 - 香农熵不等式和拉奥熵不等式，从而揭示了极限布森伯格 - 特拉维斯系统的双熵结构。
