1维零压流体运动方程组的解的局部结构

Local Structure of the Solutions to One-Dimensional Zero-Pressure Flow Equations

研究1维零压流体运动方程组,引进势函数并讨论它的最小值点.当初值(x,t)∈R×(0,∞)时,得出解的局部结构的以下结论.若势函数有唯一非退化最小值点,则(x,t)附近的解光滑;若势函数有2个以上非退化最小值点或唯一退化最小值点,则(x,t)附近的解间断.

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）∈RX （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）.