Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Two Complementary Types of Total Time Derivative in Classical Field
  Theories and Maxwell's Equations   Close insight into mathematical and conceptual structure of classical field
theories shows serious inconsistencies in their common basis. In other words,
we claim in this work to have come across two severe mathematical blunders in
the very foundations of theoretical hydrodynamics. One of the defects concerns
the traditional treatment of time derivatives in Eulerian hydrodynamic
description. The other one resides in the conventional demonstration of the
so-called Convection Theorem. Both approaches are thought to be necessary for
cross-verification of the standard differential form of continuity equation.
Any revision of these fundamental results might have important implications for
all classical field theories. Rigorous reconsideration of time derivatives in
Eulerian description shows that it evokes Minkowski metric for any flow field
domain without any previous postulation. Mathematical approach is developed
within the framework of congruences for general 4-dimensional differentiable
manifold and the final result is formulated in form of a theorem. A modified
version of the Convection Theorem provides a necessary cross-verification for a
reconsidered differential form of continuity equation. Although the approach is
developed for one-component (scalar) flow field, it can be easily generalized
to any tensor field. Some possible implications for classical electrodynamics
are also explored.

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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
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The categories of this paper are: q-fin
2
The categories of this paper are: math
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: hep-th