Local well-posedness of the multi-layer shallow-water model with free surface

Ronan Monjarret

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arXiv · 1411.2342

Local well-posedness of the multi-layer shallow-water model with free surface

Ronan Monjarret

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Abstract

In this paper, we address the question of the hyperbolicity and the local well- posedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in H^s(R^2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this model and prove a more general criterion of hyperbolicity and local well-posedness, under a particular asymptotic regime and a weak stratification assumptions of the densities and the velocities. Finally, we consider a new conservative multi-layer shallow water model, we prove the symmetrizability, the hyperbolicity and the local well-posedness and rely it to the basic multi-layer shallow water model.

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Ronan Monjarret. 2014-11-10. Local well-posedness of the multi-layer shallow-water model with free surface. https://arxiv.org/abs/1411.2342

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