Eigenvalue problem for the Navier-Stokes equations

Hi, I´m trying to solve the eigenvalue problem for the Navier-Stokes equations in a 2D configuration.

I’ve tried the method explained in the FreeFem manual but i haven’t find a way to adapt it to a problem with more than one function. Also, the problem has the peculiarity that pressure isn’t time dependent so the matrices have a special shape. I couldn’t find any example for this.

If someone knew how to solve it or knows an example where this problem is treated, it would be very helpful.

Thanks in advance

You can have a look at the code (and paper) in the following repository, especially the file Eigensolver.edp. It’s in 3D, but should be easily adapted to 2D (in fact I need to do that for an upcoming FreeFEM tutorial). Let me know if you have some specific questions.