1,292 research outputs found
3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system
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 for
subsonic flows. Due to the nonzero swirl, the main difficulties lie in the
solvability of a singular elliptic equation which concerns the angular
component of the vorticity in its cylindrical representation, and in analysis
of streamlines near the axis
Structural stability of Supersonic solutions to the Euler-Poisson system
The well-posedness for the supersonic solutions of the Euler-Poisson system
for hydrodynamical model in semiconductor devices and plasmas is studied in
this paper. We first reformulate the Euler-Poisson system in the supersonic
region into a second order hyperbolic-elliptic coupled system together with
several transport equations. One of the key ingredients of the analysis is to
obtain the well-posedness of the boundary value problem for the associated
linearized hyperbolic-elliptic coupled system, which is achieved via a delicate
choice of multiplier to gain energy estimate. The nonlinear structural
stability of supersonic solution in the general situation is established by
combining the iteration method with the estimate for hyperbolic-elliptic system
and the transport equations together.Comment: The paper was revised substantially in this new version. In
particular, we constructed the new multiplier under general conditions on the
background solution
Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations
In this paper, both structural and dynamical stabilities of steady transonic
shock solutions for one-dimensional Euler-Poission system are investigated.
First, a steady transonic shock solution with supersonic backgroumd charge is
shown to be structurally stable with respect to small perturbations of the
background charge, provided that the electric field is positive at the shock
location. Second, any steady transonic shock solution with the supersonic
background charge is proved to be dynamically and exponentially stable with
respect to small perturbation of the initial data, provided the electric field
is not too negative at the shock location. The proof of the first stability
result relies on a monotonicity argument for the shock position and the
downstream density, and a stability analysis for subsonic and supersonic
solutions. The dynamical stability of the steady transonic shock for the
Euler-Poisson equations can be transformed to the global well-posedness of a
free boundary problem for a quasilinear second order equation with nonlinear
boundary conditions. The analysis for the associated linearized problem plays
an essential role
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