The Cauchy problem for the two dimensional Euler–Poisson system

Li, Dong, and Wu, Yifei. "The Cauchy problem for the two dimensional Euler–Poisson system." Journal of the European Mathematical Society 016.10 (2014): 2211-2266. <http://eudml.org/doc/277780>.

@article{Li2014,
abstract = {The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system. In this work we completely settle the 2D Cauchy problem.},
author = {Li, Dong, Wu, Yifei},
journal = {Journal of the European Mathematical Society},
keywords = {Euler-Poisson system; Klein-Gordon system; normal form transformation; global well-posedness; Euler-Poisson system; Klein-Gordon system; normal form transformtion; global well-posedness},
language = {eng},
number = {10},
pages = {2211-2266},
publisher = {European Mathematical Society Publishing House},
title = {The Cauchy problem for the two dimensional Euler–Poisson system},
url = {http://eudml.org/doc/277780},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Li, Dong
AU - Wu, Yifei
TI - The Cauchy problem for the two dimensional Euler–Poisson system
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 10
SP - 2211
EP - 2266
AB - The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system. In this work we completely settle the 2D Cauchy problem.
LA - eng
KW - Euler-Poisson system; Klein-Gordon system; normal form transformation; global well-posedness; Euler-Poisson system; Klein-Gordon system; normal form transformtion; global well-posedness
UR - http://eudml.org/doc/277780
ER -