Strong solutions of the thin film equation in spherical geometry

2017/09/29 by Roman M. Taranets, Taranets, Roman M.
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1709.10496

openalex publication_date 2017/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile.

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