Cartesian vector solutions for $ N $-dimensional non-isentropic Euler equations with Coriolis force and linear damping

Xitong Liu; Xiao Yong Wen; Manwai Yuen; Xitong Liu; Xiao Yong Wen; Manwai Yuen

doi:10.3934/math.2023877

AIMS Mathematics

2023, Volume 8, Issue 7: 17171-17196. doi: 10.3934/math.2023877

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Cartesian vector solutions for $ N $-dimensional non-isentropic Euler equations with Coriolis force and linear damping

1.
Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong, China
2.
School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received: 03 March 2023 Revised: 27 March 2023 Accepted: 27 March 2023 Published: 17 May 2023
MSC : 35C05, 35Q31, 76B03, 76M60

In this paper, we construct and prove the existence of theoretical solutions to non-isentropic Euler equations with a time-dependent linear damping and Coriolis force in Cartesian form. New exact solutions can be acquired based on this form with examples presented in this paper. By constructing appropriate matrices $ A(t) $, and vectors $ {\mathbf{b} }(t) $, special cases of exact solutions, where entropy $ s = \ln\rho $, are obtained. This is the first matrix form solution of non-isentropic Euler equations to the best of the authors' knowledge.
- non-isentropic fluids,
- Euler equations,
- Coriolis force,
- linear-damping symmetric and anti-symmetric matrices,
- curve integration,
- Cartesian vector form solutions
Citation: Xitong Liu, Xiao Yong Wen, Manwai Yuen. Cartesian vector solutions for $ N $-dimensional non-isentropic Euler equations with Coriolis force and linear damping[J]. AIMS Mathematics, 2023, 8(7): 17171-17196. doi: 10.3934/math.2023877

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Abstract

In this paper, we construct and prove the existence of theoretical solutions to non-isentropic Euler equations with a time-dependent linear damping and Coriolis force in Cartesian form. New exact solutions can be acquired based on this form with examples presented in this paper. By constructing appropriate matrices $ A(t) $, and vectors $ {\mathbf{b} }(t) $, special cases of exact solutions, where entropy $ s = \ln\rho $, are obtained. This is the first matrix form solution of non-isentropic Euler equations to the best of the authors' knowledge.

References

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