# Given Curl V, can you find V?

1. Apr 24, 2010

### Jerbearrrrrr

Say V is a vector field.
Is there a way (or rather a reasonable algorithm) to find V, given Curl V?

Thanks

2. Apr 24, 2010

### Office_Shredder

Staff Emeritus
If I told you curlV=0, can you give me a bunch of different functions that satisfy this requirement?

3. Apr 24, 2010

### Jerbearrrrrr

Okay, let's impose V satisfies boundary conditions on a (hyper)surface or something. (Though I don't remember the conditions for uniqueness and regularity and so on of PDE solutions)

I guess I asked the wrong question.
Is there a way to find V within a transformation in what we might call the Kernel of the curl operator?

(Like when someone asks what differentiates to f, it's understood that we can add a constant...)

4. Apr 25, 2010

### g_edgar

Yes, if the domain is good enough. The conventional way to phrase the problem is: given a vector field T with div T = 0, find V so that curl V = T. This should be in all multivariable calculus textbooks. But perhaps only after the discussion of vector integration.

5. Apr 25, 2010

### arildno

You can determine V out of its curl, up to an arbitrary gradient field.