The global classical solution to compressible Euler system with velocity alignment

Lining Tong; Li Chen; Simone Göttlich; Shu Wang; Lining Tong; Li Chen; Simone Göttlich; Shu Wang

doi:10.3934/math.2020429

AIMS Mathematics

2020, Volume 5, Issue 6: 6673-6692. doi: 10.3934/math.2020429

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Research article

The global classical solution to compressible Euler system with velocity alignment

1.
Department of Mathematics, Shanghai University, 200244, P. R. China
2.
Department of Mathematics, University of Mannheim, 68131 Mannheim, Germany
3.
School of Mathematics and Information Sciences, Guangzhou University, 510006, P. R. China
4.
School of Mathematics, Faculty of Science, Beijing University of Technology, 100124, P. R. China

Received: 29 June 2020 Accepted: 06 August 2020 Published: 28 August 2020
MSC : 35L65, 35Q70

In this paper, the compressible Euler system with velocity alignment and damping is considered, where the influence matrix of velocity alignment is not positive definite. Sound speed is used to reformulate the system into symmetric hyperbolic type. The global existence and uniqueness of smooth solution for small initial data is provided.
- non-local velocity alignment,
- global existence,
- nonlinear pressure
Citation: Lining Tong, Li Chen, Simone Göttlich, Shu Wang. The global classical solution to compressible Euler system with velocity alignment[J]. AIMS Mathematics, 2020, 5(6): 6673-6692. doi: 10.3934/math.2020429

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Abstract

In this paper, the compressible Euler system with velocity alignment and damping is considered, where the influence matrix of velocity alignment is not positive definite. Sound speed is used to reformulate the system into symmetric hyperbolic type. The global existence and uniqueness of smooth solution for small initial data is provided.

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