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On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion
- Source :
- SIAM Journal on Mathematical Analysis. 52:1232-1289
- Publication Year :
- 2020
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2020.
-
Abstract
- 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 freeslip and include Navier's slip as well as stick-slip. Both steady and unsteady flows of such fluids in three-dimensional domains are analyzed.
- Subjects :
- Cauchy stress tensor
Velocity gradient
Applied Mathematics
Weak solution
Mathematical analysis
Fluid Dynamics (physics.flu-dyn)
Mathematics::Analysis of PDEs
FOS: Physical sciences
Physics - Fluid Dynamics
Physics::Fluid Dynamics
Computational Mathematics
Mathematics - Analysis of PDEs
Monotone polygon
76A02, 76A05, 76D03, 35Q35
Incompressible flow
FOS: Mathematics
Boundary value problem
Analysis
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- ISSN :
- 10957154 and 00361410
- Volume :
- 52
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Mathematical Analysis
- Accession number :
- edsair.doi.dedup.....396c14de1985e88427930f808b366626