Investigating spatial-temporal correlations, specifically how spatial points vary over time, is crucial for understanding point cloud videos. Traditional methods, particularly flow-based techniques, struggle with these correlations due to the unordered spatial arrangement of sequential point cloud data. To address this challenge, we propose a novel approach that regularizes spatial-temporal correlation learning by formulating the problem as a solvable Partial Differential Equation (PDE). While PDEs have long been effective in the physical domain, their application to novel sequential data like point cloud video remains underexplored. Inspired by fluid analysis, we construct a simplified PDE, and the process of solving PDE is guided and refined by a contrastive learning structure between the temporal embeddings and the spatial embeddings. With this extra supervision, our method, named MotionPDE, serves as an effective, plug-and-play enhancement module for existing backbone models, adding minimal computational overhead and parameters. Capitalizing on the contrastive learning process, we delve deeper into the self-supervised capabilities of MotionPDE, yielding promising results that underscore its utility and adaptability in point cloud video data interpretation. The code repo with trained checkpoints will be available at https://github.com/zhh6425/motionpde.git for facilitating future research.