# American Institute of Mathematical Sciences

July & August  2021, 20(7&8): 2421-2440. doi: 10.3934/cpaa.2021079

## Three-dimensional supersonic flows of Euler-Poisson system for potential flow

 1 Department of Mathematical Sciences, KAIST, 291 Daehak-Ro, Yuseong-Gu, Daejeon 34141, Republic of Korea 2 Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-Gu, Seoul 02455, Republic of Korea 3 Center for Mathematical Analysis and Computation (CMAC), Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea

* Corresponding author

Received  February 2021 Revised  March 2021 Published  July & August 2021 Early access  May 2021

Fund Project: The first author is supported in part by Samsung Science and Technology Foundation under Project Number SSTF-BA1502-51. The second author is supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT and MOE) (No. 2015R1A5A1009350 and No. 2020R1I1A1A01058480)

We prove the unique existence of supersonic solutions of the Euler-Poisson system for potential flow in a three-dimensional rectangular cylinder when prescribing the velocity and the strength of electric field at the entrance. Overall, the main framework is similar to [1], but there are several technical differences to be taken care of vary carefully. And, it is our main goal to treat all the technical differences occurring when one considers a three dimensional supersonic solution of the steady Euler-Poisson system.

Citation: Myoungjean Bae, Hyangdong Park. Three-dimensional supersonic flows of Euler-Poisson system for potential flow. Communications on Pure & Applied Analysis, 2021, 20 (7&8) : 2421-2440. doi: 10.3934/cpaa.2021079
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