Persistent Volume Claims (PVCs) in a containerized environment allow for the automatic provisioning of storage for containers. PVCs ensure that the data remains available and persistent across container restarts and deployments, making it the correct solution for maintaining dynamic user data for a stateful application. Dynamic NFS mounts, while being suitable for file sharing, are not as seamlessly integrated with container orchestrators for automatic provisioning. Local storage is inherently non-persistent across node failures or redeployment. In-memory data grids are designed for high-speed data access and are not necessarily persistent or suitable for the scenario described.