Quantitative derivation of a two-phase porous media system from the one-velocity Baer–Nunziato and Kapila systems

• Published in: Nonlinearity Vol. 37; no. 7; pp. 75002 - 75056
• Main Authors: Crin-Barat, Timothée, Shou, Ling-Yun, Tan, Jin
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.07.2024
• Subjects: 35B40; 35Q35; 76N10; 76T17; Analysis of PDEs; Baer–Nunziato system; critical regularity; Kapila system; Mathematics; multi-fluid system; overdamping phenomenon; pressure-relaxation limit; two-phase flow in porous media; overdamping phenomenon; Baer-Nunziato system 2020 Mathematics Subject Classification-35Q35 35B40 76N10 76T17; pressure-relaxation limit; two-phase flow in porous media; Baer-Nunziato system 2020 Mathematics Subject Classification-35Q35; 35B40; 76T17; critical regularity; Multi-fluid system; 76N10; Kapila system

We derive a novel two-phase flow system in porous media as a relaxation limit of compressible multi-fluid systems. Considering a one-velocity Baer–Nunziato system with friction forces, we first justify its pressure-relaxation limit toward a Kapila model in a uniform manner with respect to the time-r...