Abstract
In this paper, we study the compressible bipolar Euler-Poisson equations with a non-flat doping profile in three-dimensional space. The existence and uniqueness of the non-constant stationary solutions are established under the smallness assumption on the gradient of the doping profile. Then we show the global existence of smooth solutions to the Cauchy problem near the stationary state provided the $H^3$ norms of the initial density and velocity are small, but the higher derivatives can be arbitrarily large.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have