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# A KdV-type Boussinesq system: From the energy level to analytic spaces

• Considered here is the well-posedness of a KdV-type Boussinesq system modeling two-way propagation of small-amplitude long waves on the surface of an ideal fluid when the motion is sensibly two dimensional. Solutions are obtained in a range of Sobolev-type spaces, from the energy level to the analytic Gevrey spaces. In addition, a criterion for detecting the possibility of blow-up in finite time in terms of loss of analyticity is derived.
Mathematics Subject Classification: Primary: 35Q35, 35Q53, 35A07; Secondary: 76B07, 76B15.

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