摘要
In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the smooth solution through the direct method in the case 0 〈 θ 〈 -θ=arctan 1/（√2＋√5）, where θ is the half angle of the wedge. Furthermore, they get the uniform C^1,1 estimates of the solution to the expansion problem.
基金
supported by the National Natural Science Foundation of China(No.11371240)
Shanghai Municipal Education Commission of Scientific Research Innovation Project(No.11ZZ84)
the Fundamental Research Funds for the Central Universities(No.15CX02074A)
the grant of “the First-Class Discipline of Universities in Shanghai”
