2024/11/06 by Sam Cuthbertson, Cuthbertson, Sam, Glen Wheeler +3
Engineering · #53E40 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Differential Geometry (math.DG) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.2411.03579
openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the anisotropic curve shortening flow in the plane in the presence of an ambient force. We consider force fields in which all their derivatives are bounded in the L∞ sense. We prove that closed embedded curves that have a minimum of curvature sufficiently large shrink to round points. The method of proof follows along the same lines of Gage and Hamilton, in that we study a rescaling to prove curvature bounds. We additionally show that the influence of an ambient force field may make such a result untrue, by giving sufficient conditions on the ambient field that ensures eventual non-convexity of an initially convex curve evolving under the flow.