Global existence and asymptotic behavior of the solutions to the 3D bipolar non-isentropic Euler–Poisson equation
Articles
Yeping Li
East China University of Science and Technology
Published 2015-07-20
https://doi.org/10.15388/NA.2015.3.1
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Keywords

non-isentropic bipolar Euler–Poisson system
asymptotic behavior
Green function
smooth solution
energy estimates

How to Cite

Li, Y. (2015) “Global existence and asymptotic behavior of the solutions to the 3D bipolar non-isentropic Euler–Poisson equation”, Nonlinear Analysis: Modelling and Control, 20(3), pp. 305–330. doi:10.15388/NA.2015.3.1.

Abstract

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.

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