| Abstract: |
| In this presentation, we will discuss techniques to improve the time of existence for dispersive water waves equations while keeping the small parameters $(\epsilon,\mu)$ decoupled. The proofs rely on the energy method and new Strichartz estimates. These techniques are robust and can be adapted to several dispersive equations and systems. In the two-dimensional case, we exceed the time of existence of order $\epsilon^{-1}$ in the long wave regime, which appears to be new. The talk is based on joint work with Benjamin Melinand, Didier Pilod, Sigmund Selberg, and Achenef Tesfahun. |
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