Compression effects in heterogeneous media

0505707 - MÚ 2020 RIV FR eng J - Journal Article
Bresch, D. - Nečasová, Šárka - Perrin, Ch.
Compression effects in heterogeneous media.
Journal de l'École Polytechnique Mathématiques. Roč. 6, June (2019), s. 433-467. ISSN 2429-7100. E-ISSN 2270-518X
R&D Projects: GA ČR GA16-03230S; GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : compressible Brinkman equations * maximal packing * singular limit * free boundary
OECD category: Pure mathematics
Method of publishing: Open access
http://dx.doi.org/10.5802/jep.98

We study in this paper compression effects in heterogeneous media with maximal packing constraint. Starting from compressible Brinkman equations, where maximal packing is encoded in a singular pressure and a singular bulk viscosity, we show that the global weak solutions converge (up to a subsequence) to global weak solutions of the two-phase compressible/incompressible Brinkman equations with respect to a parameter ε which measures effects close to the maximal packing value. Depending on the importance of the bulk viscosity with respect to the pressure in the dense regimes, memory effects are activated or not at the limit in the congested (incompressible) domain.
Permanent Link: http://hdl.handle.net/11104/0297122