Weak solutions to a nonlinear variational sine–Gordon equation

This paper considers a nonlinear variational sine–Gordon equation utt−c(u)[c(u)ux]x+λ22sin(2u)=0 which describes the motion of long waves on a neutral dipole chain in the continuum limit and a few other physical phenomena. We establish the global existence of dissipative weak solutions to its Cauchy problem for initial data in the space H1×L2H1×L2 by using the Young measure theory in the setting of LpLp spaces.