In this paper, we focus on the two-dimensional subsonic flow problem around an infinite long ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by a second elliptic equation. By the use of a separation variable method, Strum- Liouville theorem and scaling technique, we show that a nontriviM subsonic flow around the infinite long ramp does not exist under some certain assumptions on the potential flow with a low Mach number.
In this paper, under the generalized conservation condition of mass flux in a unbounded domain, we are concerned with the global existence and stability of a perturbed subsonic circulatory flow for the two-dimensional steady Euler equation, which is assumed to be isentropic and irrotational. Such a problem can be reduced into a second order quasi-linear elliptic equation on the stream function in an exterior domain with a Dirichlet boundary value condition on the circular body and a stability condition at infinity. The key ingredient is establishing delicate weighted Hlder estimates to obtain the infinite behaviors of the flow under physical assumption.
