| Abstract: |
| We study a problem modelling steady water-waves generated by an obstacle in an N-layer fluid. As in the Neumann-Kelvin problem, our model is a linearized version of the steady-free surface Euler`s equations around a rest state. We end-up with an elliptic problem involving interface conditions. Depending on the parameters, we can define several regimes. In the two-layer case (water/air) there are two regimes: the super-critical regime in which a finite energy solution exists, and a sub-critical regime in which a wake appears, and forms as to decompose the solution into a finite energy part and an oscillatory part (Pierotti, 2008). We aim to generalize these methods to solve the N-layer problem. We will show the existence of a unique solution for almost all parameters of the problem, and we will outline some numerical methods that can be built on this theory. |
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