Existence and stability of dissipative turbulent solutions to a simple bi-fluid model of compressible fluids

0548752 - MÚ 2022 RIV CH eng J - Journal Article
Jin, B. - Kwon, Y.-S. - Nečasová, Šárka - Novotný, A.
Existence and stability of dissipative turbulent solutions to a simple bi-fluid model of compressible fluids.
Journal of Elliptic and Parabolic Equations. Roč. 7, č. 2 (2021), s. 537-570. ISSN 2296-9020
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : compressible fluid * bi-fluid model * non-linear viscous fluid
OECD category: Pure mathematics
Method of publishing: Limited access
https://doi.org/10.1007/s41808-021-00137-6

Following Abbatiello et al. (DCCDS-A 41(1):1–28, 2020), we introduce dissipative turbulent solutions to a simple model of a mixture of two non interacting compressible fluids filling a bounded domain with general non zero inflow/outflow boundary conditions. We prove existence of such solutions for all adiabatic coefficients γ> 1 , their compatibility with classical solutions, the relative energy inequality, and the weak–strong uniqueness principle in this class. The class of dissipative turbulent solutions is so far the largest class of generalized solutions which still enjoys the weak–strong uniqueness property.
Permanent Link: http://hdl.handle.net/11104/0324820