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October  2010, 26(4): 1121-1139. doi: 10.3934/dcds.2010.26.1121

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

Jerry L. Bona 1, , Zoran Grujić 2, and  Henrik Kalisch 3,

1. 

Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, United States
2. 

Department of Mathematics, University of Virginia, Charlottesville, VA 22904
3. 

Department of Mathematics, University of Bergen, 5008 Bergen, Norway

Received  March 2009 Revised  May 2009 Published  December 2009

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.
Keywords: Boussinesq systems, Gevrey-space analysis., two-way propagation of water waves, analyticity, well-posedness for nonlinear dispersive equations.
Mathematics Subject Classification: Primary: 35Q35, 35Q53, 35A07; Secondary: 76B07, 76B1.
Citation: Jerry L. Bona, Zoran Grujić, Henrik Kalisch. A KdV-type Boussinesq system: From the energy level to analytic spaces. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1121-1139. doi: 10.3934/dcds.2010.26.1121
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