Hi,(adsbygoogle = window.adsbygoogle || []).push({});

An issue has come up in my research: I think the problem can be phrased as such:

Given a differential equation of the form

[tex]Lu(t) = f(t)[/tex]

Where the forcing function is of the form [tex]f(t)=\gamma e^{-t/\epsilon},\gamma[/tex] is a constant, and L is some linear second order operator.

We want to see what happens to the particular solution in the limit as [tex]\epsilon \to 0[/tex] while keeping

[tex]\int_{0}^{\infty}f(t')dt' = const[/tex]

Physically, it seems as if the forcing function will turn into a boundary condition, although I am not sure how to make this rigorous. Is this always the case? When I go through and evaluate the limits for the particular solution I am finding results that do not make sense.

In case a particular example helps, this is where this problem comes from.

Consider the time independent linearized Navier Stokes equation for a viscous rotating fluid with forcing. The equation governing the dynamics is:

[tex] u_{zz}-\frac{if}{\nu} u =-\frac{1}{\nu} A(z) [/tex]

where [tex]A(z)=\gamma e^{-z/\epsilon}[/tex]

I am getting results that do make sense physically for particular types of forcing functions A, so I would like to see what happens when A turns into a surface condition as opposed to a forcing function, since I know what to expect in that case.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Differential Equation with forcing/fluids question

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**