Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K"ahler Geometry and the Navier-Stokes Equations   We study the Navier-Stokes and Euler equations of incompressible
hydrodynamics in two and three spatial dimensions and show how the constraint
of incompressiblility leads to equations of Monge--Amp\`ere type for the stream
function, when the Laplacian of the pressure is known. In two dimensions a
K\"ahler geometry is described, which is associated with the Monge--Amp\`ere
problem. This K\"ahler structure is then generalised to `two-and-a-half
dimensional' flows, of which Burgers' vortex is one example. In three
dimensions, we show how a generalized Calabi--Yau structure emerges in a
special case.

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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph