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Comparison of solutions of Boussinesq systems

  • Youcef Mammeri EMAIL logo and Yumeng Zhang
Published/Copyright: May 9, 2014

Abstract.

We compare the solution of the generalized Boussinesq systems, for various values of a,b,c,d, ηt+ux+ε((ηu)x+auxxx-bηxxt)=0, ut+ηx+ε(uux+cηxxx-duxxt)=0. These systems describe the two-way propagation of small amplitude long waves in shallow water. We prove, using an energy method introduced by Bona, Pritchard and Scott [Fluid Dynamics in Astrophysics and Geophysics, American Mathematical Society, Providence (1983), 235–267], that respective solutions of Boussinesq systems, starting from the same initial datum, remain close on a time interval inversely proportional to the wave amplitude.

Received: 2014-3-3
Revised: 2014-4-11
Accepted: 2014-4-23
Published Online: 2014-5-9
Published in Print: 2014-6-1

© 2014 by Walter de Gruyter Berlin/Boston

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