Nonlinear smoothing implies improved lower bounds on the radius of spatial analyticity for nonlinear dispersive equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909692914040832 |
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| author | Baldasso, Mikaela Correia, Simão |
| author_facet | Baldasso, Mikaela Correia, Simão |
| contents | We provide a roadmap to establish improved lower bounds on the decay rate of the uniform radius of analyticity $σ(T)$ for a given nonlinear dispersive equation, reducing the problem to the derivation of nonlinear smoothing estimates with a specific distribution of extra derivatives. We apply this strategy for both the defocusing generalized KdV and the nonlinear Schrödinger equations with odd pure-power nonlinearity. For both equations, we reach the lower bound $σ(T)\gtrsim T^{-\frac{1}{2}-ε}$, for any $ε>0$, thus improving all available results in the current literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear smoothing implies improved lower bounds on the radius of spatial analyticity for nonlinear dispersive equations Baldasso, Mikaela Correia, Simão Analysis of PDEs We provide a roadmap to establish improved lower bounds on the decay rate of the uniform radius of analyticity $σ(T)$ for a given nonlinear dispersive equation, reducing the problem to the derivation of nonlinear smoothing estimates with a specific distribution of extra derivatives. We apply this strategy for both the defocusing generalized KdV and the nonlinear Schrödinger equations with odd pure-power nonlinearity. For both equations, we reach the lower bound $σ(T)\gtrsim T^{-\frac{1}{2}-ε}$, for any $ε>0$, thus improving all available results in the current literature. |
| title | Nonlinear smoothing implies improved lower bounds on the radius of spatial analyticity for nonlinear dispersive equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.13083 |