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arXiv · 2507.11837

Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip

Changfeng Gui·David Ruiz·Chunjing Xie·Huan Xu
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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].

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Changfeng Gui, David Ruiz, Chunjing Xie, Huan Xu. 2025-07-16. Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip. https://arxiv.org/abs/2507.11837

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