# Understanding the Navier-Stokes equations

#### ChaosTheory

Hi everybody!

I'm studying physics (13th grade) and I'm doing some external research and I've been really interested by fluid dynamics, more specifically the Navier-Stokes equations. I want to learn more about them but I don't know where to begin.

I've started by teaching myself vector calculus and vector fields (I'm learning div, curl and grad). I've also researched tensors but I'm a bit confused on

a. how many different equations there are
b. how they are derived (I've seen derivations from F = ma and other ways).

Thanks!

#### topsquark

Forum Staff
Hi everybody!

I'm studying physics (13th grade) and I'm doing some external research and I've been really interested by fluid dynamics, more specifically the Navier-Stokes equations. I want to learn more about them but I don't know where to begin.

I've started by teaching myself vector calculus and vector fields (I'm learning div, curl and grad). I've also researched tensors but I'm a bit confused on

a. how many different equations there are
b. how they are derived (I've seen derivations from F = ma and other ways).

Thanks!
Fluid dynamics is a very active branch of Physics and it's good that you are showing interest. You could have a good career doing just that.

On the other hand, the Navier-Stokes equations are non-linear partial differential equations. Unless you are using some kind of approximation to them? (My field of expertise is in Quantum Field Theory. The Math can be, well, horrible. Be warned: Fluid dynamics equations are worse. You are going to have to take a lot of Math.)

-Dan

#### ChaosTheory

• 