3 research outputs found
Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows
For a two-dimensional steady supersonic Euler flow past a convex cornered
wall with right angle, a characteristic discontinuity (vortex sheet and/or
entropy wave) is generated, which separates the supersonic flow from the gas at
rest (hence subsonic). We proved that such a transonic characteristic
discontinuity is structurally stable under small perturbations of the upstream
supersonic flow in . The existence of a weak entropy solution and Lipschitz
continuous free boundary (i.e. characteristic discontinuity) is established. To
achieve this, the problem is formulated as a free boundary problem for a
nonstrictly hyperbolic system of conservation laws; and the free boundary
problem is then solved by analyzing nonlinear wave interactions and employing
the front tracking method.Comment: 26 pages, 3 figure