Type: Article

Time decay estimates for solutions of the Cauchy problem for the modified Kawahara equation

Naumkin, Pavel I.;

Abstract:

The large-time behaviour of solutions of the Cauchy problem for the modified Kawahara equation {ut??xu3?a3?3xu+b5?5xu=0,(t,x)?R2, u(0,x)=u0(x),x?R, where a,b>0, is investigated. Under the assumptions that the total mass of the initial data ?u0(x)dx is nonzero and the initial data u0 are small in the norm of H2,1 it is proved that a global-in-time solution exists and estimates for its large-time decay are found.