Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Do the Navier-Stokes equations embody all physics in a flow of Newtonian
  fluids?   The Navier-Stokes equations are the governing equations of fluid flows. They
are deemed to embody all physics in a flow of Newtonian fluids like water,
especially when we assume the fluid is incompressible. Fluid flows are usually
described in the Eulerian perspective wherein we focus on the fluid's
quantities at a fixed point in space as time processes, rather than the motion
of each individual particle. The latter perspective is indeed the Lagrangian
perspective which is widely used in solid mechanics like elasticity. Thus, the
Navier-Stokes equations should be and indeed they are always used in the
Eulerian perspective. Here we show the right-hand sides of the Navier-Stokes
equations were derived not in the Eulerian perspective but rather in the
Lagrangian perspective, because the strain rates used in the derivation were
the Lagrangian Cauchy strain rates. Thus, for describing fluid flows in the
Eulerian perspective, the Navier-Stokes equations may lost some physics. To
make it sure, we put the Cauchy strain into the material derivative, and then
derive the Eulerian Cauchy strain rates. We find the difference between the
Eulerian and the Lagrangian Cauchy strain rates is significant when in a
turbulent flow. Therefore, On the basis of the Eulerian Cauchy strain rates, we
derive a new set of governing equations for the flow of Newtonian fluids. The
newly derived governing equations are fully in the Eulerian perspective. We
believe they are the real equations that Navier, Cauchy, Poisson and Stokes
intended to find for the viscous flow of Newtonian fluids.

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The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int