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arXiv · 1206.3756

On the Cauchy problem for a Boussinesq type system

Felipe Linares·Mahendra Panthee·Jorge Drumond Silva
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Abstract

We consider the initial value problem (IVP) associated to a Boussinesq type system. After rewriting the system in an equivalent form of coupled KdV-type equations, we prove that this is locally well-posed in $(H^s(\R^2))^4$, $s>3/2$, using sharp smoothing estimates. Consequently we obtain the local well-posedness result for the original system in $H^s\times \mathcal{V}^{s+1}$ for $s>3/2$ (see below for the definition of $\mathcal{V}^{s}$).

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Felipe Linares, Mahendra Panthee, Jorge Drumond Silva. 2012-06-17. On the Cauchy problem for a Boussinesq type system. https://arxiv.org/abs/1206.3756

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