A self similar solution is developed for two dimensional, steady, isentropic and inviscid flow. Some fundamental properties are clarified for centered simple waves R and shock waves S. The present paper provides furth...A self similar solution is developed for two dimensional, steady, isentropic and inviscid flow. Some fundamental properties are clarified for centered simple waves R and shock waves S. The present paper provides further theoretical analysis to clarify the results obtained by Glimm et al. using theoretical and computational methods. 展开更多
The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular po...The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular point in the configuration of the solution.The interactions of at most two incoming waves are dealt with in this paper, and all six kinds of configurations for the solutions are obtained. They are the Mach reflection (one kind), the shock wave S transmits contact discontinuity J (two kinds), the overtaking of two incoming shock waves (two kinds), and the collision of two incoming shock waves (one kind). 展开更多
The Cauchy problem of high-dimensional hyperbolic systems of nonlinear equations with initial data have been considered. Under certain assumptions on the eigenvalues of the nonlinear systems and the initial data, we g...The Cauchy problem of high-dimensional hyperbolic systems of nonlinear equations with initial data have been considered. Under certain assumptions on the eigenvalues of the nonlinear systems and the initial data, we get two theorems about the existence of global smooth solutions.展开更多
文摘A self similar solution is developed for two dimensional, steady, isentropic and inviscid flow. Some fundamental properties are clarified for centered simple waves R and shock waves S. The present paper provides further theoretical analysis to clarify the results obtained by Glimm et al. using theoretical and computational methods.
文摘The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular point in the configuration of the solution.The interactions of at most two incoming waves are dealt with in this paper, and all six kinds of configurations for the solutions are obtained. They are the Mach reflection (one kind), the shock wave S transmits contact discontinuity J (two kinds), the overtaking of two incoming shock waves (two kinds), and the collision of two incoming shock waves (one kind).
文摘The Cauchy problem of high-dimensional hyperbolic systems of nonlinear equations with initial data have been considered. Under certain assumptions on the eigenvalues of the nonlinear systems and the initial data, we get two theorems about the existence of global smooth solutions.
