Myoungjean Bae

In this paper, we prove the existence and stability of subsonic flows for a steady full Euler--Poisson system in a two-dimensional nozzle of finite length when imposing the electric potential difference on a noninsulated boundary from a fixed point at the entrance, and prescribing pressure at the exit of the nozzle. The Euler--Poisson system for subsonic flow is a hyperbolic-elliptic coupled nonlinear system. One of the crucial ingredients of this work is the combination of Helmholtz decompositi

We address the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler–Poisson system in a cylinder supplemented with non-small boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3-D axisymmetric flow with a nonzero swirl (= angular momentum density) component. With the newly introduced decomposition, a quasilinear elliptic system of second order is derived from the elliptic modes in Euler–Poisson system f

We present our recent results on the Prandtl-Meyer reflection for supersonic potential flow past a solid ramp. When a steady supersonic flow passes a solid ramp, there are two possible configurations: the weak shock solution and the strong shock solution. Elling-Liu’s theorem (2008) indicates that the steady supersonic weak shock solution can be regarded as a long-time asymptotic state of an unsteady flow for a class of physical parameters determined by certain assumptions for potential flow. In

We investigate two-dimensional steady Euler–Poisson system which describes the motion of compressible self-gravitating flows. The unique existence and stability of subsonic flows in a duct of finite length are obtained when prescribing the entropy at the entrance and the pressure at the exit. After introducing the stream function, the Euler–Poisson system can be decomposed into several transport equations and a second-order nonlinear elliptic system. We discover an energy estimate for the associ

In this paper, we prove structural stability of contact discontinuities for full Euler system.

<p style="text-indent:20px;">We prove the unique existence of supersonic solutions of the Euler-Poisson system for potential flow in a three-dimensional rectangular cylinder when prescribing the velocity and the strength of electric field at the entrance. Overall, the main framework is similar to [<xref ref-type="bibr" rid="b1">1</xref>], but there are several technical differences to be taken care of vary carefully. And, it is our main goal to treat all the technical differences occurring when

We prove the existence of a subsonic weak solution $({u}, \rho, p)$ to a steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy $(= \frac{p}{\rho^{\gamma}})$ at the entrance by a piecewise $C^2$ function with a discontinuity at a point. Due to the variable entropy condition with a discontinuity at the entrance, the corresponding solution has a nonzero vorticity and contains a contact discontinuity $x_2=g_D(x_1)$. We construct such a solution via

We are concerned with the Prandtl-Meyer reflection configurations of unsteady global solutions for supersonic flow impinging upon a symmetric solid wedge. Prandtl (1936) first employed the shock polar analysis to show that there are two possible steady configurations: the steady weak and strong shock solutions, when a steady supersonic flow impinges upon the wedge whose angle is less than the detachment angle, and then conjectured that the steady weak shock solution is physically admissible. The

Given constant data of density $ρ_0$, velocity $-u_0{\bf e}_r$, pressure $p_0$ and electric force $-E_0{\bf e}_r$ for supersonic flow at the entrance, and constant pressure $p_{\rm ex}$ for subsonic flow at the exit, we prove that Euler-Poisson system admits a unique transonic shock solution in a two dimensional convergent nozzle, provided that $u_0&gt;0$, $E_0&gt;0$, and that $E_0$ is sufficiently large depending on $(ρ_0, u_0, p_0)$ and the length of the nozzle.

We establish the unique existence and stability of supersonic flow for steady Euler-Poisson system in a two dimensional rectangular domain when prescribing pressure, incoming flow angles, and normal electric field at the entrance. With the aid of Helmholtz decomposition for the velocity field, the supersonic flows of the Euler-Poisson system are obtained as solutions to a nonlinear system consisting of a second order hyperbolic-elliptic coupled system and several transport equations. The new fea

We prove the existence of a subsonic weak solution $({\bf u}, ρ, p)$ to steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy $(= \frac{p}{ρ^γ})$ at the entrance by a piecewise $C^2$ function with a discontinuity at a point. Due to the variable entropy condition with a discontinuity at the entrance, the corresponding solution has a nonzero vorticity and contains a contact discontinuity $x_2=g_D(x_1)$. We construct such a solution via Helmholtz