Applications and Novel Regularization of the Thin-Film Equation
<|reference_start|>Applications and Novel Regularization of the Thin-Film Equation: The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel regularization of the thin-film equation to model droplet spreading. The solution of the regularized thin-film equation -- the Geometric Thin-Film Equation is studied and characterized. Two robust numerical solvers are discussed, notably, a fast and mesh-free numerical scheme for simulating thin-film flows in two and three spatial dimensions. Moreover, we prove the regularity and convergence of the numerical solutions. The existence and uniqueness of the solution of the Geometric Thin-Film Equation with respect to a wide range of measure-valued initial conditions are also discussed.<|reference_end|>
@article{pang2024applications,
    title={Applications and Novel Regularization of the Thin-Film Equation},
    author={Khang Ee Pang},
    journal={arXiv preprint arXiv:2409.17187},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.17187},
    primaryClass={physics.flu-dyn cs.NA math.NA}
}