Existence of the Rotational Subsonic Stationary Solution for a Two-Dimensional Bipolar Euler-Poisson Equation

In this paper, we study a two-dimensional bipolar Euler-Poisson equation (hydrodynamic model), which arises in mathematical modeling for semiconductors and plasmas. We are interested in the existence of the rotational subsonic stationary solution. Under the proper boundary conditions, we show the existence of rotational subsonic stationary solutions for the two-dimensional bipolar Euler-Poisson equation. This result is the first result about the rotational subsonic stationary solution for the multi-dimensional bipolar isentropic Euler-Poisson equation. The proof is completed by delicate energy estimate and fixed point principle.