Several sufficient conditions on the absence of global solutions of the fifth-order KdV equations with L1(R) initial data

This paper studies the absence of the global solutions to the fifth-order KdV equations in the form, ∂tu+∂x5u=b1u∂xu+c1∂xu∂x2u+c2u∂x3u,x∈R,t∈R+.As the initial data u(0,x)∈L1(R), the coefficients b1>−c1 and c1=c2<0, we use the method of nonlinear capacity, developed by Galaktionov, Pokhozhaev and Mitidieri, and obtain several sufficient conditions of nonexistence of global solutions.