Abstract: This paper is concerned with one-dimensional zero-pressure flow equations.By introducing a potential function and discussing its minimizing point,the following conclusions on the local structure of the solution are drawn for each point (x,t)∈R×(0,∞).When potential function has a uniqe non-degenerate minimizing point,solutions are smooth in the neighborhood of (x,t);When potential function has more than two non-degenerate minimizing points or a uniqe degenerate minimizing point,solutions are discontinuous in the neighborhood of (x,t).

Key words: zero-pressure flow equations, local structure, degenerate point, non-degenerate point