Abstract
In this paper, we give a systematic study for the initialand boundary problem of linear convection-diffusion equationsin the zero viscosity limit. The well-posed boundary conditions are classified to analyze the corresponding solution structures and the boundary layer behavior. The results confirm thatthe Neumann type of far-field boundary condition is preferred.Under some appropriate regularity and compatibility conditions on the initial and boundary datas, we obtain optimal error estimates between the full viscous solution and the inviscid solution with suitable boundary layer corrections. This model well describes the behavior at the far field for many physical and engineering systems such as fluid dynamical equations and electro-magnetic equations. The results obtained here should provide some theoretical guidance for designing effective far field boundary conditions.