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GLOBAL C1 SOLUTION OF CAUCHY PROBLEM FOR TWO-DIMENSIONAL GAS DYNAMICS SYSTEM
陆云光
数学物理学报(英文版). 1993 (1):
65-73.
Using the method of characteristic lines this paper considers the global C1 solution of the Cauchy problem for two-dimensional gas dynamics system. When the initial data degenerate to the special case ρ0(x, y)=const, the global C1 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 C1 solution is also obtained in this case when the initial data of the forms (ρ0(x, y), u0(x, y), v0(x, y))=(exp(ω01 (c1x+d1y)+ω02(c2x+d2y)), u01(c1x+d1y)+u02(c2x+d2y), u01(c1x+d1y)+u02(c2x+d2y)), where ci and di(i=1, 2) are constants.
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