Locally bounded linear differential operators

[greentea28a]

The following is a problem statement.

locally bounded (or locally (weakly) compact) differential operators of the Schwartz space of smooth functions on a sigma-compact manifold

I realize this is very abstract. I expect the solution to be just as abstract.

Thanks in advance.

 

[Number Nine]

That's not a question, and we're not in the habit of doing people's work for them anyway. What is the problem you're working on, and what have you done so far?

 

[greentea28a]

I believe the above problem is the core of the Navier-Stokes equation. It describes the inner working of the NS equations from a mathematical operator's point-of-view.

I have studied bornology from Hogbe-Nlend's books Bornology and Functional Analysis; Nuclear and Conuclear Spaces. According to Wikipedia, bornology is the minimum amount of structure to address boundedness of sets and functions.

The next closest thing I have come across is Nuclear Convex Bornological Spaces.

 

[Number Nine]

I believe the above problem is the core of the Navier-Stokes equation.

What problem? You just said a kind of operator. It would be like me starting a thread and saying "bounded linear function". What are you trying to prove?