期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 52, 期 2, 页码 1232-1289出版社
SIAM PUBLICATIONS
DOI: 10.1137/19M1244895
关键词
implicit constitutive theory; generalized viscosity; generalized fluidity; stress power-law fluid; shear thinning/shear thickening fluids; activated fluids; activation criterion; boundary conditions; slip; activated boundary conditions; long-time and large-data existence theory; weak solution
资金
- programme ERC-CZ - Ministry of Education, Youth and Sports of the Czech Republic [LL1202]
- Grant Agency of the Czech Republic [GA CR 18-12719S]
In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids, Navier-Stokes fluids, classical power-law fluids as well as stress power-law fluids, and their various generalizations including the fluids that we refer to as activated fluids, namely, fluids that behave as an Euler fluid prior activation and behave as a viscous fluid once activation takes place. We also present a classification concerning boundary conditions that are viewed as the constitutive relations on the boundary. In the second part of the paper, we develop a robust mathematical theory for activated Euler fluids associated with different types of the boundary conditions ranging from no-slip to free-slip and include Navier's slip as well as stick-slip. Both steady and unsteady flows of such fluids in three-dimensional domains are analyzed.
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