Cartesian vector solutions for $ N $-dimensional non-isentropic Euler equations with Coriolis force and linear damping-Reference-Cited by-同舟云学术

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

Published:2023 Issue:7 Volume:8 Page:17171-17196
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Liu Xitong¹,Wen Xiao Yong²,Yuen Manwai¹

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference40 articles.

1. M. Ghil, S. Childress, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics, New York: Springer-Verlag, 1987. https://doi.org/10.1007/978-1-4612-1052-8

2. J. Pedlosky, Geophysical Fluid Dynamics, New York: Springer-Verlag, 1987. https://doi.org/10.1007/978-1-4612-4650-3

3. J. Marshall, R. A. Plumb, Atmosphere, Ocean, and Climate Dynamics: An Introductory Text, San Diego, CA: Academic Press, 2008.

4. F. V. Dolzhansky, Fundamentals of Geophysical Hydrodynamics, Berlin, Heidelberg: Springer, 2013. https://doi.org/10.1007/978-3-642-31034-8

5. H. Liu, E. Tadmor, Rotation prevents finite-time breakdown, Phys. D, 188 (2004), 262–276. https://doi.org/10.1016/j.physd.2003.07.006