Smoothing Estimates for Weakly Nonlinear Internal Waves in a Rotating Ocean
We study the effect of rotation on the smoothing properties of the KdV type equations on the real line. Smoothing refers to a scattering-like property that the nonlinear part of the equation is smoother than the initial data, and thus many futures of the linear evolution can be extended to the nonli...
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| Datum: | 2024 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1082 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | We study the effect of rotation on the smoothing properties of the KdV type equations on the real line. Smoothing refers to a scattering-like property that the nonlinear part of the equation is smoother than the initial data, and thus many futures of the linear evolution can be extended to the nonlinear one. Smoothing in the case of the KdV equation with periodic boundary conditions is a result of the presence of high frequency waves that weaken the nonlinearity through time averaging [1,12]. It is crucial for this phenomena that the zero Fourier mode can be removed due to the conservation of the mean. On the real line this mechanism breaks down as the resonance sets close to zero frequency are sizable and normal form transformations are not useful [21], and hence smoothing fails. The model we study is a perturbation of the KdV equation on a rotating frame of reference.
Mathematical Subject Classification 2020: 35Q53 |
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