GLOBAL WEAK SOLUTIONS TO THE α-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS

doi:10.1007/s10473-021-0303-1

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 679-702.doi: 10.1007/s10473-021-0303-1

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GLOBAL WEAK SOLUTIONS TO THE α-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS

Yabo REN¹, Boling GUO², Shu WANG¹

1. Faculty of Science, Beijing University of Technology, Beijing 100124, China;
2. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China

Received:2019-04-11 Revised:2020-10-27 Online:2021-06-25 Published:2021-06-07
Contact: Yabo REN E-mail:ryb2018@emails.bjut.edu.cn
About author:Boling GUO,E-mail:gbl@iapcm.ac.cn;Shu WANG,E-mail:wangshu@bjut.edu.cn
Supported by:
This work was supported by National Science Foundation of China (11901020), Beijing Natural Science Foundation (1204026), and the Science and Technology Project of Beijing Municipal Commission of Education China (KM202010005027).

Abstract

Abstract: Global in time weak solutions to the $\alpha$-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to $\alpha$-model regularization for the three dimension compressible Euler-Poisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies $\gamma>\frac{4}{3}$.

Key words: Global weak solutions, $\alpha$-model regularization for Euler-Poisson equations, Faedo-Galerkin method

CLC Number:

35Q85

Yabo REN, Boling GUO, Shu WANG. GLOBAL WEAK SOLUTIONS TO THE α-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS[J].Acta mathematica scientia,Series B, 2021, 41(3): 679-702.

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GLOBAL WEAK SOLUTIONS TO THE α-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS

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