A Note On Determining Projections for Non-Homogeneous Incompressible Fluids
| Autor: | Faktor, Benjamin, Holst, Michael |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this note, we consider a viscous incompressible fluid in a finite domain in both two and three dimensions, and examine the question of determining degrees of freedom (projections, functionals, and nodes). Our particular interest is the case of non-constant viscosity, representing either a fluid with viscosity that changes over time (such as an oil that loses viscosity as it degrades), or a fluid with viscosity varying spatially (as in the case of two-phase or multi-phase fluid models). Our goal is to apply the determining projection framework developed by the second author in previous work for weak solutions to the Navier-Stokes equations, in order to establish bounds on the number of determining functionals for this case, or equivalently, the dimension of a determining set, based on the approximation properties of an underlying determining projection. The results for the case of time-varying viscosity mirror those for weak solutions established in earlier work for constant viscosity. The case of space-varying viscosity, treated within a single-fluid Navier-Stokes model, is quite challenging to analyze, but we explore some preliminary ideas for understanding this case. Comment: 20 pages, no figures |
| Databáze: | arXiv |
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