On a nonlocal Cahn-Hilliard/Navier-Stokes system with degenerate mobility and singular potential for incompressible fluids with different densities
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, ISSN: 0294-1449, Vol: 38, Issue: 3, Page: 647-687
2021
- 16Citations
- 1Captures
Metric Options: Counts1 Year3 YearSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Article Description
We consider a diffuse interface model describing flow and phase separation of a binary isothermal mixture of (partially) immiscible viscous incompressible Newtonian fluids having different densities. The model is the nonlocal version of the one derived by Abels, Garcke and Grün and consists in a inhomogeneous Navier-Stokes type system coupled with a convective nonlocal Cahn-Hilliard equation. This model was already analyzed in a paper by the same author, for the case of singular potential and non-degenerate mobility. Here, we address the physically more relevant situation of degenerate mobility and we prove existence of global weak solutions satisfying an energy inequality. The proof relies on a regularization technique based on a careful approximation of the singular potential. Existence and regularity of the pressure field is also discussed. Moreover, in two dimensions and for slightly more regular solutions, we establish the validity of the energy identity. We point out that in none of the existing contributions dealing with the original (local) Abels, Garcke Grün model, an energy identity in two dimensions is derived (only existence of weak solutions has been proven so far).
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0294144920300846; http://dx.doi.org/10.1016/j.anihpc.2020.08.005; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85091497481&origin=inward; https://ems.press/doi/10.1016/j.anihpc.2020.08.005; https://dx.doi.org/10.1016/j.anihpc.2020.08.005; https://ems.press/journals/aihpc/articles/4077249
European Mathematical Society - EMS - Publishing House GmbH
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know