Well-posedness of transonic characteristic discontinuities in two-dimensional steady compressible Euler flows |
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Authors: | Gui-Qiang Chen Vaibhav Kukreja Hairong Yuan |
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Institution: | 1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China 2. Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK 3. Department of Mathematics, Northwestern University, Evanston, IL, 60208, USA 4. Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil 5. Department of Mathematics, East China Normal University, Shanghai, 200241, China
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Abstract: | In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total variation of the incoming supersonic flow over a solid right wedge. It is a free boundary problem in Eulerian coordinates and, across the free boundary (characteristic discontinuity), the Euler equations are of elliptic–hyperbolic composite-mixed type. In this paper, we further prove that such a transonic characteristic discontinuity solution is unique and L 1–stable with respect to the small perturbation of the incoming supersonic flow in Lagrangian coordinates. |
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