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...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.展开更多
基金supported by the National Natural Science Foundation of China(No.11371240)Shanghai Municipal Education Commission of Scientific Research Innovation Project(No.11ZZ84)+1 种基金the Fundamental Research Funds for the Central Universities(No.15CX02074A)the grant of “the First-Class Discipline of Universities in Shanghai”
文摘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.
