Solve pde with two variables through fenics

General
1

Hi all,

I am trying to solve a set of PDEs. It has two variables, which I can not find a proper solvers in Finics. Can anyone give me some advice on how to get the weak form and solve it in Fenics. The following picture is the PDEs.
image

Thanks
Yongqiang

2

You can simple use a mixed function space. Ses for instance Mixed formulation for the Poisson equation — DOLFINx 0.8.0 documentation

3

Thank you, Jeremy.
Is it okay to multiply a test function for each PDE to drive the weak form although each of them contains two variables?

Thanks,
Yongqiang

4

Yes, see for instance: Stokes equations using Taylor-Hood elements — DOLFINx 0.8.0 documentation