Energy conservative solutions to the system of full variational sine-Gordon equations in a unit sphere

Abstract

We establish the global existence of a conservative weak solution to the Cauchy problem for a complete system of variational sine-Gordon equations, which models the motion of long waves on a neutral dipole chain in the continuum limit in a unit sphere. Although singularities may develop in finite time, the energy of the solution is conserved across singular times. We also obtain the continuous dependence of solutions on the given initial data.