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Embedding the Boussinesq equations in the incompressible Euler equations on a manifold

The Boussinesq equations for inviscid, incompressible two-dimensional fluid flow in the presence of gravity are given by

where is the velocity field, is the pressure field, and is the density field (or, in some physical interpretations, the temperature field). 1,694 more words


Heat flow and zeroes of polynomials

Let be a monic polynomial of degree with complex coefficients. Then by the fundamental theorem of algebra, we can factor as

for some complex zeroes (possibly with repetition). 761 more words