Nontrivial weak solutions of the stationary KdV equation in sharp $L^p$ spaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917337906544640 |
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| author | Pathak, Mandon |
| author_facet | Pathak, Mandon |
| contents | In this paper we utilize a convex integration scheme to construct non-trivial solutions to the stationary KdV equation which lie in $L^p(\mathbb{T})$, $p < 2$. In addition, we demonstrate this result is sharp in the sense that if $u \in L^2(\mathbb{T})$ is a weak solution then $u \in C^\infty(\mathbb{T})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12555 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nontrivial weak solutions of the stationary KdV equation in sharp $L^p$ spaces Pathak, Mandon Analysis of PDEs Classical Analysis and ODEs In this paper we utilize a convex integration scheme to construct non-trivial solutions to the stationary KdV equation which lie in $L^p(\mathbb{T})$, $p < 2$. In addition, we demonstrate this result is sharp in the sense that if $u \in L^2(\mathbb{T})$ is a weak solution then $u \in C^\infty(\mathbb{T})$. |
| title | Nontrivial weak solutions of the stationary KdV equation in sharp $L^p$ spaces |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.12555 |