Pullback attractors and statistical solutions for the lattice Zakharov equations on time-dependent spaces

In this paper, the authors investigate the probability distribution of solutions within the time-dependent phase spaces for the lattice Zakharov equations with varying coefficients via the pullback attractors and the notion of generalized Banach limits. They firstly show that the addressed initial value problem is globally well-posed and prove that the related evolution process has a time-dependent pullback attractor on the time-dependent phase spaces. Then they construct a family of invariant Borel probability measures with supports contained in the pullback attractor. Furthermore, they prove that the constructed family of invariant measures is a statistical solution for the addressed lattice Zakharov equations and that Liouville's theorem holds true.