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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.22142 |
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Table of Contents:
- We study the two-dimensional gravity water waves with a one-dimensional interface with small initial data. Our main contributions include the development of two novel localization lemmas and a Transition-of-Derivatives method, which enable us to reformulate the water wave system into the following simplified structure: $$(D_t^2-iA\partial_α)θ=i\frac{t}α|D_t^2ζ|^2D_tθ+R$$ where $R$ behaves well in the energy estimate. As a key consequence, we derive the uniform bound $$ \sup_{t\geq 0}\Big(\norm{D_tζ(\cdot,t)}_{H^{s+1/2}}+\norm{ζ_α(\cdot,t)-1}_{H^s}\Big)\leq Cε, $$ which enhances existing global uniform energy estimates for 2D water waves by imposing less restrictive constraints on the low-frequency components of the initial data.