Fluid Relaxation Approximation of the Busenberg–Travis Cross-Diffusion System
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.
Authors
- José A. Carrillo (ORCID: https://orcid.org/0000-0001-8819-4660)
- Bo Du (ORCID: https://orcid.org/0000-0002-0059-8458)
- Ansgar Jüngel (ORCID: https://orcid.org/0000-0003-0633-8929)
- Xiuqing Chen (ORCID: https://orcid.org/0000-0002-6982-2155)
Institutions
- TU Wien (AT)
- Sun Yat-sen University (CN)
- Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) (CN)
- Mathematical Institute of the Slovak Academy of Sciences (SK)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2025-06-03
- DOI
- https://doi.org/10.1007/s00220-025-05341-2
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- National Natural Science Foundation of China
- Austrian Science Fund
- Engineering and Physical Sciences Research Council
- European Research Council
- Agencia Estatal de Investigación