2020/10/28 by Tania Pernas-Castaño, Juan J. L. Velázquez, Pernas-Castaño, Tania +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2010.15180
openalex publication_date 2020/10/28 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28
In this work we will study the dynamics of a thin layer of a viscous fluid\nwhich is embedded in the interior of another viscous fluid. The resulting flow\ncan be approximated by means of the solutions of a free boundary problem for\nthe Stokes equation in which one of the unknowns is the shape of a curve which\napproximates the geometry of the thin layer of fluid. We also derive the\nequation yielding the thickness of this fluid. This model, that will be termed\nas the Geometric Free Boundary Problem, will be derived using matched\nasymptotic expansions. We will prove that the Geometric Free Boundary Problem\nis well posed and the solutions of the thickness equation are well defined (in\nparticular they do not yield breaking of fluid layers) as long as the solutions\nof the Geometric Free Boundary Problem exist.\n