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We derive the hydrodynamic limit of the Kawasaki dynamics for theone-dimensional conservative system of unbounded real-valued spins witharbitrary strong, quadratic and finite-range interactions. This extends priorresults for non-interacting spin systems. The result is obtained by adaptingtwo scale approach of Grunewald, Otto, Villani and Westdickenberg combined withthe authors' recent approach on conservative systems with strong interactions.

Hydrodynamic limit of the Kawasaki dynamics on the 1D-lattice with strong, finite-range interaction