The Generalized Riemann Problem Of Euler Equations For Zero Pressure Flow

In this paper,we study the Riemann problem and the generalized Riemann problem of Euler equations for zero pressure flow.We study the existence of the Borel measure solution,the Ladon measure solution and the measure solution in the sense of LebesgueStieltjes integral.For the Borel measure-valued solution and the Ladon measure-valued solution,we obtain two different forms of generalized R-H conditions by their definitions,and then we obtain the existence of the solution;for the measure-valued solution in the sense of Lebesgue-Stieltjes integral,we construct the solution directly by using the generalized potential and obtain the existence of the solution.Finally,we find that the results obtained by these three definitions are consistent by comparison.