Existence theorem for homogeneous incompressible Navier-Stokes equation with variable rheology. (English) Zbl 1408.76024
Summary: We look at a homogeneous incompressible fluid with a time and space variable rheology of Bingham type, which is governed by a coupling equation. Such a system is a simplified model for a gas-particle mixture that flows under the influence of gravity. The main application of this kind of model are pyroclastic flows in the context of volcanology. In order to prove long time existence of weak solutions, a classical Galerkin approximation method coupled with a priori estimates allows us to partially solve the problem. A difficulty remains with the stress tensor, which must satisfy an implicit constitutive relation. Some numerical simulations of a flow of this type are given in the last section. These numerical experiments highlight the influence of the fluidization phenomenon in the flow.
MSC:
| 76A10 | Viscoelastic fluids |
| 76A20 | Thin fluid films |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35Q30 | Navier-Stokes equations |
Keywords:
weak solution; existence result; variable rheology; Bingham fluids; Galerkin method; monotone graphReferences:
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