| Abstract: |
| This talk is concerned with a class of higher-order models for the unidirectional propagation of small amplitude long waves on the surface of an ideal fluid.
In the water waves context, the Boussinesq and Korteweg-de Vries models are proven to be good approximations of the two-dimensional Euler equation
in regimes where their derivation is valid. However, the time scale of their validity extends only to about ten wavelengths or so.
The second-order models considered here are formally accurate on the order of a hundred wavelengths.
We will show an extended version of global well-posedness in $H^1$.
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