Nontrivial weak solutions of the stationary KdV equation in sharp $L^p$ spaces

Mandon Pathak

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arXiv · 2603.12555

Nontrivial weak solutions of the stationary KdV equation in sharp $L^p$ spaces

Mandon Pathak

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Abstract

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 $u \in C^\infty(\mathbb{T})$.

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Mandon Pathak. 2026-03-13. Nontrivial weak solutions of the stationary KdV equation in sharp $L^p$ spaces. https://arxiv.org/abs/2603.12555

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