GLOBAL SUBSONIC JET WITH STRONG TRANSONIC SHOCK OVER A CONVEX CORNERED WEDGE FOR THE TWO-DIMENSIONAL STEADY FULL EULER EQUATIONS

For a uniformly supersonic flow past a convex cornered wedge with the pressure being given for the surrounding quiescent gas at the downstream, as shown in experimental results, it is expected to form a shock followed by a contact discontinuity, which is also called the jet flow. By the shock polar analysis, it is well-known that there are two possible shocks, one a strong shock and the other one a weak shock. The strong shock is always transonic, while the weak shock could be transonic or supersonic. In this paper, we prove the global existence, asymptotic behaviors, uniqueness, and stability of the subsonic jet with a strong transonic shock under the perturbation of the upstream flow and the pressure of the surrounding quiescent gas, for the two-dimensional steady full Euler equations. We first formulate the problem into a nonlinear problem with two free boundaries meeting at the wedge corner, and formulate the boundary conditions on them. Then we introduce a modified Lagrange coordinates transformation to straighten the two free boundaries at the same time, and study the elliptic estimate with proper weighted Holder norms to deal with the wedge corner singularity and the asymptotic behaviors for the Euler equations in the Lagrangian coordinates carefully, and then design an iteration scheme based on the estimates.