The Continuity Equation

This post is revised by Chat GPT. This post presents a detailed walkthrough of the continuity equation from physical intuition to mathematical formalism. We aim to derive the equation step by step and explain all quantities involved. 1. Motivation: Conservation in Physical Systems Many physical quantities are conserved in nature. For instance: Mass in a closed system Charge in electromagnetic systems Energy in isolated systems Number of particles in fluid dynamics ...

June 17, 2025