Resumen de Global existence and decay of solutions of a coupled system of BBM-Burgers equations

Jardel Morais Pereira

• 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 Hs(R) x Hs(R) for s > - 2 is studied. Furthermore we find decay estimates of the solutions of in the norm Lq(R) x Lq(R), 2 < - q < - for general initial data provided that a32b2<1 and p|3. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.