Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip
Analysis of PDEs
2025-07-17 v1
Abstract
This paper focuses on establishing the existence of a class of steady solutions, termed least total curvature solutions, to the incompressible Euler system in a strip. The solutions obtained in this paper complement the least total curvature solutions already known. Our approach employs a minimization procedure to identify a monotone heteroclinic solution for a conveniently chosen semilinear elliptic PDE. This method also enables us to construct positive and monotone (and consequently stable) solutions to semilinear elliptic PDEs with non-convex superlevel sets in a strip domain. This can be regarded as a negative answer to a generalized problem raised in [27].
Keywords
Cite
@article{arxiv.2507.11837,
title = {Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip},
author = {Changfeng Gui and David Ruiz and Chunjing Xie and Huan Xu},
journal= {arXiv preprint arXiv:2507.11837},
year = {2025}
}