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timeant

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Are there any references?

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- Thread starter timeant
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timeant

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Are there any references?

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A. Sommerfeld, Lectures of Theoretical Physics, vol. 3

- #3

timeant

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Electrodynamics. Lectures on Theoretical Physics, Vol. 3 by Arnold Sommerfeld

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DrClaude

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timeant

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We all know that charge conservation is one of necessary conditions for the existence of Maxwell equations!

I want to know: is charge conservation one of sufficient conditions for the existence of Maxwell equations?

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- #7

timeant

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rigorous math literature ? Really ?

By bing.com, I cannot find the existene of field equations.

For electromagnetic field, is the charge conservation (##\partial_\alpha J^\alpha=0##) one of sufficient conditions for the existence of Maxwell equations?

For gravitational field, is the soure's conservation (##\nabla_\alpha T^{\alpha\beta}=0##) one of sufficient conditions for the existence of Einstein field equations?

As an analogy, for ##\nabla\cdot \mathbf{u}=\rho, \nabla\times \mathbf{u}=\mathbf{S}##, is ##\nabla\cdot \mathbf{S}=0## one of sufficient conditions for the existence of div-curl system?

I think so! They are all sufficient conditions.

The EXISTENCE should be talked, e.g. http://www.claymath.org/millennium-problems/navier–stokes-equation

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timeant

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Junichi Aramaki, L^p Theory for the div-curl System, Int. Journal of Math. Analysis, Vol. 8, 2014, no. 6, 259 - 271. http://dx.doi.org/10.12988/ijma.2014.4112 ) says that : div B =0 is one of sufficient conditions of existence.

Maxwell equations are double div--curl systems. I think that the charge continuity equation is also one of sufficient conditions of existence.

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