摘要
Using the method of characteristic lines this paper considers the global C^1 solution of the Cauchy problem for two-dimensional gas dynamics system. When the initial data degenerate to the special case φ_0(x, y)=const, the global C^1 solution is obtained. For the case of isentropic exponent γ=1, a transformation about variables is introduced, which changes the system to a first order linear hyperbolic system with constant coefficients and the global C^1 solution is also obtained in this case when the initial data of the forms (φ_0(x, y), u_0(x, y), u_0(x, y))=(exp(w_(01) (c_1x+d_1y)+w_(02)(c_2x+d_2y)), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y)), where c_i and d_i(i=1, 2) are constants.
Using the method of characteristic lines this paper considers the global C^1 solution of the Cauchy problem for two-dimensional gas dynamics system. When the initial data degenerate to the special case φ_0(x, y)=const, the global C^1 solution is obtained. For the case of isentropic exponent γ=1, a transformation about variables is introduced, which changes the system to a first order linear hyperbolic system with constant coefficients and the global C^1 solution is also obtained in this case when the initial data of the forms (φ_0(x, y), u_0(x, y), u_0(x, y))=(exp(w_(01) (c_1x+d_1y)+w_(02)(c_2x+d_2y)), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y)), where c_i and d_i(i=1, 2) are constants.
