Global Solution of an Initial-Value Problem for Two-Dimensional Compressible Euler Equations

  title={Global Solution of an Initial-Value Problem for Two-Dimensional Compressible Euler Equations},
  author={Jiequan Li},
  journal={Journal of Differential Equations},
  • Jiequan Li
  • Published 10 February 2002
  • Mathematics
  • Journal of Differential Equations
Abstract This paper is concerned with the existence of global continuous solutions of the expansion of a wedge of gas into a vacuum for compressible Euler equations. By hodograph transformation, we first prove that the flow is governed by a partial differential equation of second order, which is further reduced to a system of two nonhomogeneous linearly degenerate equations in the phase space under an irrotationality condition. Then this conclusion is applied to solving the problem that a wedge… 

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Preface Preliminaries Geometry of Characteristics and Discontinuities Riemann Solution Geometry of Conservation Laws Scalar Conservation Laws One-Dimensional Scalar Conservation Laws The Generalized