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<p>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.</p>

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Fluid Relaxation Approximation of the Busenberg–Travis Cross-Diffusion System

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月3日

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  • José Antonio Carrillo,
  • Xiuqing Chen,
  • Bang Du,
  • Ansgar Jüngel

摘要

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.