Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911059274629120 |
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| author | Gui, Changfeng Ruiz, David Xie, Chunjing Xu, Huan |
| author_facet | Gui, Changfeng Ruiz, David Xie, Chunjing Xu, Huan |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip Gui, Changfeng Ruiz, David Xie, Chunjing Xu, Huan Analysis of PDEs 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]. |
| title | Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.11837 |