Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition
Analysis of PDEs
2025-06-26 v2 Mathematical Physics
math.MP
Abstract
It has been established that solutions to the inviscid Proudman-Johnson equation subject to a homogeneous three-point boundary condition can develop singularities in finite time. In this paper, we consider the possibility of singularity formation in solutions of the generalized, inviscid Proudman-Johnson equation with damping subject to the same homogeneous three-point boundary condition. In particular, we derive conditions the initial data must satisfy in order for solutions to blowup in finite time with either bounded or unbounded smooth damping term.
Keywords
Cite
@article{arxiv.2106.00068,
title = {Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition},
author = {Ikechukwu Obi-Okoye and Alejandro Sarria},
journal= {arXiv preprint arXiv:2106.00068},
year = {2025}
}