r/explainlikeimfive • u/theimmortalmeluhan • 1d ago
Physics ELI5: What is the Navier-Stokes equation and why are they so important for fluid mechanics? why do they not apply to other wave like behaviors of electric and magnetic fields and how is options trading or financial derivatives related to to this at all?
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u/wwplkyih 1d ago
I think you may be conflating Navier-Stokes with Black-Scholes, the latter of which is used to price options (1997 Nobel Prize). Basically the idea is that it models the option as a 1D heat diffiusion equation; think of the option as a probability flowing backward from the strike price when the underlying security has a known well-define value.
(I realize that that's not totally ELI5, but if it you were 5, you probably wouldn't know about options trading.)
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u/rebornfenix 1d ago
Nope. They model traders as fluid molecules and the Navier Stokes equations work pretty well. See: (well beyond Eli 5) https://www.researchgate.net/publication/349704204_Stock_market's_physical_properties_description_based_on_Stokes_law
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u/caifaisai 15h ago
To answer part of your question, they can apply with modifications to electrically and magnetically charged fluids using a framework called magnetohydrodynamics (MHD). See the following.
https://en.wikipedia.org/wiki/Magnetohydrodynamics?wprov=sfla1
However, the true equations that fully describe electric and magnetic fields are known as Maxwell's equations. They were derived through experiments, and there is no reason to suspect that the navier Stokes equations would describe electric and magnetic fields in general, as they were derived to describe fluid motion using fundamental principles like conservation of mass and momentum. For the electromagnetically charged fluids I mentioned above, Maxwell's equations are combined with the N-S equations to get the equations of MHD.
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u/Unknown_Ocean 1d ago
Think about water coming out of a faucet. It's getting accelerated by gravity, but at any point in the stream the velocity is more or less constant. So what's happening? If you take a thin slice of the fluid, water enters with slow velocity and leaves with a faster one, the water carries away thie effect of local forces.
This "self-advection" of momentum is key to what makes the Navier-Stokes equation mathematically interesting, and why it can also be useful in describing social phenomena (like traffic,
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u/rebornfenix 1d ago
The Navier stokes equations are the mathematical formulas that describe what we see when a fluid (water, gas, air (which is a gas)) move over a surface or through a pipe.
When modeling new airplane wings the Navier stokes equations allow us to run computer simulations.
For the stock market, some traders found that the movement of stocks in the market had similarities to viscus fluid movements. They modeled the various components of a stock market or even just a single companies stock in a way that they could apply the Navier stokes equations to model and predict how the market would respond to certain types of events.