| Abstract: |
| The full (irrotational Euler) equations for the motion of water waves can be difficult to implement computationally. A popular alternative is to study truncated series models, in which the Dirichlet-to-Neumann operator is expanded as a series, and an approximate system is formed by truncating this series after finitely many terms. While the full equations of motion are famously known to have a well-posed initial value problem, in joint work with Jerry Bona, David Nicholls, and Mike Siegel, we have shown that the truncated series models in fact have ill-posed initial value problems. More specifically, we identify a nonlinear backward parabolic term left in the equations after truncation which causes catastrophic growth. The work presented includes a mix of analysis and numerical results. |
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