The hydrodynamic limit is a mathematical method that derives macroscopic deterministic partial differential equations as limits from microscopic large-scale interacting systems. In Var93, Varadhan introduced a widely applicable strategy for the hydrodynamic limits, which relies on proving the so-called decomposition theorem for closed L 2 -form. Therefore, one of the keys to prove the hydrodynamic limits lies in proving Varadhan’s decomposition theorem. While this strategy has been successful in proving the hydrodynamic limit for some non-gradient systems FUY96,KLO94,Qua92,Sas10,Sas11,VY97, the proof of Varadhan’s decomposition theorem depends on the particular interacting system under consideration. However, in the recent studies by Bannai-Kametani-Sasada BKS24 and Bannai-Sasada BSa, they proved Varadhan’s decomposition theorem for a general class of large-scale interacting systems. In their framework, microscopic large-scale interacting systems are constructed by interactions. In the recent study BSb, Bannai-Sasada generalized the definition of interactions and compute the 0-th uniform cohomology. We first recall the definition of interactions.
Hidetada Wachi (Fri,) studied this question.