In this paper, we study the existence of global classical solutions and the vanishing diffusion limit of a 3D conservation laws derived from the well-known Keller-Segel model. First, we establish the global well-posedness of classical solutions to the Cauchy problem for the model with smooth initial data which is of small L (2) norm, together with some a priori estimates uniform for t and . Then, we investigate the zero diffusion limit and get the global well-posedness of classical solutions to the Cauchy problem for the non-diffusive model. Finally, we derive the convergence rate of the model...
