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arXiv · 1402.3194

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

Ronan Monjarret
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Abstract

In this paper, we adress the question of the hyperbolicity and the local well-posedness of the two-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 $\mathcal{H}^s(\mathbb{R}^2)$, 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 weak density-stratification assumption. Finally, we consider a new conservative two-layer shallow water model, prove the hyperbolicity and the local well-posedness and rely it to the basic two-layer shallow water model.

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Ronan Monjarret. 2014-02-13. Local well-posedness of the two-layer shallow water model with free surface. https://arxiv.org/abs/1402.3194

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