Manifold interpretation of Navier-Stokes equations

differential-geometry ordinary-differential-equations manifolds

Solution 1:

For the Navier Stokes equation, I am rather doubtful, because the presence of the viscosity term makes the equation not time-symmetric. And the geodesic flow is necessarily time-symmetric.

If you remove the viscosity term, you are down to the Euler equation, for which there is a well-known characterisation due to V I Arnold.

Solution 2:

Maybe Lagrangian coordinates is what you are after.

Related

Homology of the Empty set
Philosophy (Logic)
Does every ideal class contains a prime ideal that splits?
Groups with order divisible by $d$ and no element of order $d$
Can every real function be represented as two shifted even functions?
How many dimensions does a circle have?
Cohomology ring of a product
Integrating $\int\nolimits_0^{\infty}{\frac{e^{-ax}-e^{-bx}}{x}\sin{mx} \, dx} \quad (a > 0 \, , b >0)$
Number of occurrences of the digit 1 in the numbers from 0 to n
You see a route 14 bus on the moon. What is the most likely number of bus routes on the moon?
Arbitrary products of quasi-coherent sheaves?
Analytic Applications of Stone-Čech compactification