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The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas

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  • The collapse of a wedge-shaped dam containing fluid initially with a uniform velocity can be described as an expansion problem of gas into vacuum. It is an important class of binary interaction of rarefaction waves in the two dimensional Riemann problems for the compressible Euler equations. In this paper, we present various characteristic decompositions of the two dimensional pseudo-steady Euler equations for the generalized Chaplygin gas and obtain some priori estimates. By these estimates, we prove the global existence of solution to the expansion problem of a wedge of gas into vacuum with the half angle $\theta\in(0,\pi/2)$ for the generalized Chaplygin gas.
    Mathematics Subject Classification: Primary: 35L65, 35L80, 35R35, 35L60; Secondary: 35L50.


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