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$%J. Morais Pereira, Global existence and decay of solutions of a coupled system of BBM-Burgers equations, Rev. Mat. Complut. 13 (2000), no. 2, 443–423.%$

Global Existence and Decay of Solutions of a Coupled System of BBM-Burgers Equations
Jardel MORAIS PEREIRA
Universidade Federal de Santa Catarina
Departamento de Matemática
88.040-900 Florianópolis — SC, Brazil

Received: March 15, 1999
Revised: March 6, 2000

ABSTRACT

The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations

ut-uxxt- a3vxxt+ upux+ a1vpvx+ a2(upv)x- e1uxx = 0 b1vt- vxxt -b2a3uxxt+ vpvx+ b2a2upux+ b2a1(uvp)x- e2vxx = 0
(*)

in the classical Sobolev spaces 5 5 H (R)× H (R) for s> 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm q q L (R)× L (R) , 2< q < oo for general initial data provided that 2 a3b2 < 1 and p> 3 . Model (*) is motivated by a work due to Gear and Grimshaw (1984) who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.

1991 Mathematics Subject Classification: 35Q53, 35B40.