Communications in Mathematical Sciences

Volume 17 (2019)

Number 1

Global solutions of 3D partially damped Euler–Poisson two-fluid system

Pages: 1 – 32



Yi Zhou (School of Mathematical Sciences, Fudan University, Shanghai, China)

Yi Zhu (Department of Mathematics, East China University of Science and Technology, Shanghai, China)


In this paper, we prove the global existence of small solutions to partially damped Euler–Poisson “two fluid” system in three dimensional periodic domain. Different from the previous “two fluid” Euler–Poisson systems, our model describes two fluids that obey different dynamical evolutions, one is compressible Euler and another is compressible Euler with damping. We use a carefully designed time-weighted energy frame to prove our theorem.


Euler–Maxwell two-fluid model, dissipative analysis, global regularity

2010 Mathematics Subject Classification

35Q31, 35Q35, 76N10

Y. Zhu is the corresponding author.

Y. Zhou is supported by Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education of China, Shanghai, NSFC (No.11421061) and the 973 Program (No.2013CB834100). Y. Zhu is supported by NSFC (11801175), Shanghai Sailing Program (No.18YF1405500), Fundamental Research Funds for the Central Universities (No.222201814026) and China Postdoctoral Science Foundation (2018M630406).

Received 4 May 2018

Accepted 5 October 2018

Published 30 May 2019