Statistical solutions and Kolmogorov entropy for the lattice long-wave–short-wave resonance equations in weighted space

Abstract

This article studies the lattice long-wave–short-wave resonance equations in weighted spaces. The authors first prove the global well-posedness of the initial value problem and the existence of the pullback attractor for the process generated by the solution mappings in the weighted space. Then they establish that the process possesses a family of invariant Borel probability measures supported by the pullback attractor. Afterwards, they verify that this family of Borel probability measures satisfies the Liouville theorem and is a statistical solution of the lattice long-wave–short-wave resonance equations. Finally, they prove an upper bound of the Kolmogorov entropy of the statistical solution.