Global existence and asymptotic behavior of the solutions to the 3D bipolar non-isentropic Euler–Poisson equation

• Main Author: Yeping Li
• Format: Article
• Language: English
• Published: Vilnius University Press 2015-07-01
• Series: Nonlinear Analysis
• Subjects: non-isentropic bipolar Euler–Poisson system; asymptotic behavior; Green function; smooth solution; energy estimates
• Online Access: http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13516

In this paper, the global existence of smooth solutions for the three-dimensional (3D) non-isentropic bipolar hydrodynamic model is showed when the initial data are close to a constant state. This system takes the form of non-isentropic Euler–Poisson with electric field and frictional damping added to the momentum equations. Moreover, the L2-decay rate of the solutions is also obtained. Our approach is based on detailed analysis of the Green function of the linearized system and elaborate energy estimates. To our knowledge, it is the first result about the existence and L2-decay rate of global smooth solutions to the multi-dimensional non-isentropic bipolar hydrodynamic model.