%0 Journal Article %1 MR3721422 %A Escher, Joachim %A Lienstromberg, Christina %D 2018 %J J. Differential Equations %K %N 3 %P 2113--2132 %R 10.1016/j.jde.2017.10.015 %T Travelling waves in dilatant non-Newtonian thin films %U https://doi.org/10.1016/j.jde.2017.10.015 %V 264 %X In this article, the authors prove the existence of a traveling wave solution for a gravity-driven thin film of a viscous incompressible dilatant fluid coated with an insoluble surfactant. The governing system of second-order partial differential equations for the film's height h and the surfactant's concentration γ is derived by means of lubrication theory applied to the non-Newtonian Navier-Stokes equations. (Note that there exists a well-known ansatz for modeling non-Newtonian fluids see, for example, D. Klimov and A. Petrov, Arch. Appl. Mech. 70 (2000), no. 1-3, 3–16, doi:10.1007/s004199900027.) The general ansatz and the estimation of the energy of the wave solution presented here will be of interest for people working in the specific field. The present article is an excellent development in this area of research.

@article{MR3721422, abstract = {In this article, the authors prove the existence of a traveling wave solution for a gravity-driven thin film of a viscous incompressible dilatant fluid coated with an insoluble surfactant. The governing system of second-order partial differential equations for the film's height h and the surfactant's concentration γ is derived by means of lubrication theory applied to the non-Newtonian Navier-Stokes equations. (Note that there exists a well-known ansatz for modeling non-Newtonian fluids [see, for example, D. Klimov and A. Petrov, Arch. Appl. Mech. 70 (2000), no. 1-3, 3–16, doi:10.1007/s004199900027].) The general ansatz and the estimation of the energy of the wave solution presented here will be of interest for people working in the specific field. The present article is an excellent development in this area of research.}, added-at = {2023-12-05T17:17:37.000+0100}, author = {Escher, Joachim and Lienstromberg, Christina}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/29e67150ab9e653f38e3ee94c530d9f3e/simtech}, doi = {10.1016/j.jde.2017.10.015}, fjournal = {Journal of Differential Equations}, interhash = {fa949dda5875af26b559000325c300c3}, intrahash = {9e67150ab9e653f38e3ee94c530d9f3e}, issn = {0022-0396}, journal = {J. Differential Equations}, keywords = {}, mrclass = {35Q35 (35C07 35K40 35K65 76A05 76A20)}, mrnumber = {3721422}, mrreviewer = {Sergey V. Ershkov}, number = 3, pages = {2113--2132}, timestamp = {2023-12-05T17:17:37.000+0100}, title = {Travelling waves in dilatant non-{N}ewtonian thin films}, url = {https://doi.org/10.1016/j.jde.2017.10.015}, volume = 264, year = 2018 }