Low-regularity invariant measure for the complex-valued mKdV
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910059108237312 |
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| author | Lee, Zachary Pavlović, Nataša Staffilani, Gigliola Visciglia, Nicola |
| author_facet | Lee, Zachary Pavlović, Nataša Staffilani, Gigliola Visciglia, Nicola |
| contents | In this paper we consider the twice-renormalized, complex-valued modified KdV (mKdV) on the one-dimensional torus introduced by Chapouto. Our main result is the construction of an invariant measure supported at low-regularity. This work complements the work of Kenig et al., which constructed invariant measures supported in higher-regularity spaces for the non-renormalized mKdV. Due to the low-regularity of the support of the measure, we are forced to work in Fourier-Lebesgue spaces. The fact that we consider the complex-valued mKdV makes the problem more complicated than the real-valued case, which was previously considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Low-regularity invariant measure for the complex-valued mKdV Lee, Zachary Pavlović, Nataša Staffilani, Gigliola Visciglia, Nicola Analysis of PDEs In this paper we consider the twice-renormalized, complex-valued modified KdV (mKdV) on the one-dimensional torus introduced by Chapouto. Our main result is the construction of an invariant measure supported at low-regularity. This work complements the work of Kenig et al., which constructed invariant measures supported in higher-regularity spaces for the non-renormalized mKdV. Due to the low-regularity of the support of the measure, we are forced to work in Fourier-Lebesgue spaces. The fact that we consider the complex-valued mKdV makes the problem more complicated than the real-valued case, which was previously considered. |
| title | Low-regularity invariant measure for the complex-valued mKdV |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.18310 |