2007/11/03 by Jens Eggers, Marco A. Fontelos, Eggers, Jens +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Fluid Dynamics and Thin Films #Fluid dynamics and aerodynamics studies #Quantum chaos and dynamical systems #math.AP #math.DS
paper · pdf · doi:10.48550/arxiv.0711.0442
arxiv created 2007/11/03 · openalex publication_date 2007/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and where typical scales of the solution shrink to zero as the singularity is approached. Upon a similarity transformation, exact self-similar behaviour is mapped to the fixed point of a \it infinite dimensional dynamical system representing the original dynamics. We show that the dynamics close to the fixed point is a useful way classifying the structure of the singularity. Specifically, we consider various types of stable and unstable fixed points, centre-manifold dynamics, limit cycles, and chaotic dynamics.