I am solving a coupled system of PDEs using Mathematica's FEM capabilities.
Specifically, the Navier-Stokes equations with a no-flux stress-free boundary.
To do this, I need to specify a Dirichlet boundary condition that looks like
n.u = nx ux + ny uy = 0 on the boundary.
But in Mathematica this gives the warning
NDSolveValue::fembdcc: Cross-coupling of dependent variables in DirichletCondition[ ux+uy==0,x+y==0] is not supported in this version.
This is similar to a previous question. That answer gave a workaround using an added low viscosity shell matching onto a no-slip boundary. I would like to avoid this kludge.
Is there any to solve coupled Dirichlet boundary conditions in Mathematica 13.3.0?