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Sufficiently strong dispersion removes ill-posedness in truncated series models of water waves

  • * Corresponding author: David M. Ambrose

    * Corresponding author: David M. Ambrose

The second author is grateful for support from the National Science Foundation through grant DMS-1515849.

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  • Truncated series models of gravity water waves are popular for use in simulation. Recent work has shown that these models need not inherit the well-posedness properties of the full equations of motion (the irrotational, incompressible Euler equations). We show that if one adds a sufficiently strong dispersive term to a quadratic truncated series model, the system then has a well-posed initial value problem. Such dispersion can be relevant in certain physical contexts, such as in the case of a bending force present at the free surface, as in a hydroelastic sheet.

    Mathematics Subject Classification: Primary: 76B15; Secondary: 34A12, 76B07, 35S50.


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