We consider the 1D equation $$u_t + u u_x -\nu u_{xx}=1+ x (t,x) \in [0,+\infty] \times [0,1].$$
i read that
If $\nu >0.01$ the system behaves like a real second order system in space and we shall treat it like that. If \nu gets much smaller than that the system becomes a singularity perturped first order system (really one dimensional Euler) and develops boundary layers that require special attention.
I don't understand what this paragraphe means. Can any one help me and explein me please.
Merci d’avance pour votre aide. Bien cordialement