Research article

Two-dimensional pseudo-steady supersonic flow around a sharp corner for the generalized Chaplygin gas

  • Received: 03 July 2021 Revised: 23 November 2021 Accepted: 25 November 2021 Published: 18 April 2022
  • MSC : 35L65, 35J70, 35R35, 35J65

  • In this paper, the expansion problem which arises in a two-dimensional (2D) isentropic pseudo-steady supersonic flow expanding into vacuum around a sharp corner for the generalized Chaplygin gas is studied. This expanding problem catches the interaction of an incomplete centered simple wave with a backward planar rarefaction wave and the interaction of a non-planar simple wave with a rigid wall boundary of the 2D self-similar Euler equations. Using the methods of characteristic decompositions and invariant regions, we get the hyperbolicity in the wave interaction domains and prior $ C^{1} $ estimates of solutions to the two interaction problems. It follows the global existence of the solution up to infinity of the gas expansion problem.

    Citation: Aidi Yao. Two-dimensional pseudo-steady supersonic flow around a sharp corner for the generalized Chaplygin gas[J]. AIMS Mathematics, 2022, 7(7): 11732-11758. doi: 10.3934/math.2022654

    Related Papers:

  • In this paper, the expansion problem which arises in a two-dimensional (2D) isentropic pseudo-steady supersonic flow expanding into vacuum around a sharp corner for the generalized Chaplygin gas is studied. This expanding problem catches the interaction of an incomplete centered simple wave with a backward planar rarefaction wave and the interaction of a non-planar simple wave with a rigid wall boundary of the 2D self-similar Euler equations. Using the methods of characteristic decompositions and invariant regions, we get the hyperbolicity in the wave interaction domains and prior $ C^{1} $ estimates of solutions to the two interaction problems. It follows the global existence of the solution up to infinity of the gas expansion problem.



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