Another vector fields in terms of circulation and flux

[Jhenrique]

Other laws in terms of circulation and flux

Why others vector fields no are studied like the magnetic and electric fields? In other words, why others vector fields, like the gravitational and the hydrodynamic, haven't "supreme laws" based in the circulation/flux or curl/divergence?

 

[Matterwave]

Of course they are studied, have you heard of the Navier-Stokes equation? http://en.wikipedia.org/wiki/Navier-stokes_equation

 

[Jhenrique]

The navier stokes equation are much complicated for me... I don't understand anything!

Unfortunately, I wrong the topic's title, but what I want say is: in eletromagnetism, the circulation/flux or curl/divergence of the electrical/magnetical field (maxwell's equations) are the most general and supremes laws! All the the other equations are just details or particularities. So, why in other fields of the physics the vector fields haven't laws like exist in the electromagnetism? For example, let says that G represents the gravitational field, I never see an equation of kind:
$$\oint_{s} \vec{G}\cdot d\vec{s}=0$$ $$\oint\oint_{S} \vec{G}\cdot d^2\vec{S}=-km$$
That are analogous to the maxwell's equations...

 

[mattt]

Unfortunately, I wrong the topic's title, but what I want say is: in eletromagnetism, the circulation/flux or curl/divergence of the electrical/magnetical field (maxwell's equations) are the most general and supremes laws! All the the other equations are just details or particularities. So, why in other fields of the physics the vector fields haven't laws like exist in the electromagnetism? For example, let says that G represents the gravitational field, I never see an equation of kind:
$$\oint_{s} \vec{G}\cdot d\vec{s}=0$$ $$\oint\oint_{S} \vec{G}\cdot d^2\vec{S}=-km$$
That are analogous to the maxwell's equations...

What about Gauss law?

$$\oint_S\vec{g}\cdot d\vec{s} = -4\pi G M_{int}$$

 

[vanhees71]

The standard operations on vector fields always appear in many fields of physics. This is "natural" in a way, because they result from the symmetry structure of Eucldidean (three-dimensional) space and the corresponding symmetry group (semidirect product of rotations and translations).

In addition these operations like $\vec{\nabla} \cdot \vec{V}$ or $\vec{\nabla} \times \vec{V}$, div and curl of a vector field, and $\vec{\nabla} \phi$, the gradient of a scalar field, have clear intuitive meaning in physics, particularly in fluid dynamics (see one of may latest postings in this forum).

 

[Jhenrique]

What about Gauss law?

$$\oint_S\vec{g}\cdot d\vec{s} = -4\pi G M_{int}$$

It's the first time that I see this equation!

So, why the gauss law
$$\oint_S\vec{g}\cdot d\vec{S} = -4\pi G M_{int}$$
and this other law
$$\oint_{s} \vec{g}\cdot d\vec{s}=0$$
are not emphasized like the maxwell laws ?