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The statement that a property of a system does not change if the system is isolated.

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2 answers
225 views

How to understand continuity equation intuitively as Lorenz covariant?

As we know, it is natural that we derive the differential form of continuity equation $${\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {j} =0$$ from the integral form, in the view of absolu …
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How to understand continuity equation intuitively as Lorenz covariant?

I think I have some thoughts on my question after thinking for a while. Still waiting for other illuminating discussions. We cannot simply consider continuity equation as a general incompressible flow …
Hangci Du's user avatar
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1 answer
220 views

Why total derivative becomes partial when we use the differential form of continuity equation?

The integral form: $\frac{d q}{d t}+\oint_{S} \vec{j} \cdot d \vec{S}=0$ The differential form: ${\frac {\partial \rho }{\partial t}}+\nabla \cdot \vec{j} =0$ How to intuitively understand the change …
1 vote
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1k views

Why the continuity equation means constant densities of each fluid parcel?

As we know, the definition of material derivative of $\varphi$ is: $\frac{D\varphi}{Dt}\equiv \frac{\partial \varphi}{\partial t} + \mathbf{u}\cdot\nabla\varphi$. And the physical meaning of material …