Asymptotic Stability and the Forcing Term: An Analysis of Non-Newtonian Thin-Film Flows

2025/11/07 by Jinhong Zhao, Bin Guo, Zhao, Jinhong +1
Engineering · Materials Science · Chemical Engineering · #Fluid Dynamics and Thin Films #Solidification and crystal growth phenomena #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.2511.04947

Abstract

We study a class of fourth-order quasilinear degenerate parabolic equations under both time-and space-dependent and time-and space-independent forces, modeling non-Newtonian thin-film flow over a solid surface in the "complete wetting" regime. By analyzing the quantitative properties of solutions to non-autonomous differential inequalities and employing refined integral estimates, we derive two-sided convergence rate estimates for the solution. Numerical simulations are further provided to illustrate the consistency of our main results with the observed physical phenomena.

Citations

• Long-scale evolution of thin liquid films

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