Subsonic Flows for the Full Euler Equations in Half Plane
نویسنده
چکیده
We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler flows. The Euler system is reduced to a single elliptic equation for the stream function. The existence, uniqueness and asymptotic behaviors of the solutions for the reduced equation are established by Schauder fixed point argument and some delicate estimates. The existence of subsonic flows for the original Euler system is proved based on the results for the reduced equation, and their asymptotic behaviors in the far field are also obtained.
منابع مشابه
A Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).
This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...
متن کاملGlobal Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations
We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of second order in terms of the stream function. It is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently...
متن کاملOn Two-Dimensional Sonic-Subsonic Flow
A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-dimensional Euler equations for steady irrotational flows that may contain stagnation points. Only crude estimates are required for establishing compactness. It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points over an obsta...
متن کاملSubsonic Solutions for Steady Euler-Poisson System in Two-Dimensional Nozzles
In this paper, we prove the existence and stability of subsonic flows for steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed point at the entrance, and prescribing the pressure at the exit of the nozzle. The Euler-Poisson system for subsonic flow is a hyperbolic-elliptic coupled non...
متن کاملThe ellipticity principle for steady and selfsimilar polytropic potential flow∗
We prove the ellipticity principle for selfsimilar potential flows for gas dynamics. We show that the interior of a pseudo-subsonic-sonic-region of a smooth solution must be pseudo-subsonic. In fact, the pseudo-Mach number is below that of a domain-dependent function which is < 1 in the interior and ≤ 1 on the boundary. Therefore the interior must stay pseudo-subsonic under homotopy of pseudo-s...
متن کامل