Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...