Stabilization methods such as Streamline upwind Petrov–Galerkin and Galerkin-Least-Squares typically contain a stabilization parameter that looks something like

When applying this method to the Navier-Stokes equation, what is the treatment for the velocity term \mathbf{u} within \tau_{M,T}? It is a term that can bring convergence issues I think. Is it better to treat this term explicitly in a nonlinear method such as Newton? Or is it better to include it when calculating the jacobian of the entire variational form?