Cusp formation for a nonlocal evolution equation
Vu Hoang, Maria Radosz
TL;DR
This paper studies a nonlocal evolution equation inspired by fluid dynamics models, proving finite-time blowup and cusp formation, thus advancing understanding of singularity development in nonlocal PDEs.
Contribution
It introduces a new nonlocal evolution equation and establishes conditions for finite-time blowup and cusp formation, extending prior models in fluid dynamics.
Findings
Proved finite-time blowup of solutions.
Identified conditions for cusp formation.
Extended understanding of singularity in nonlocal PDEs.
Abstract
In this paper, we introduce a nonlocal evolution equation inspired by the C\'ordoba-C\'ordoba-Fontelos nonlocal transport equation. The C\'ordoba-C\'ordoba-Fontelos equation can be regarded as a model for the 2D surface quasigeostrophic equation or the Birkhoff-Rott equation. We prove blowup in finite time, and more importantly, investigate conditions under which the solution forms a cusp in finite time.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.