A method for constructing special solutions for multidimensional generalization of Euler equations with Coriolis force

The compressible Euler equations in Rᴺ with Coriolis force is the fundamental mathematical model for the atmospheric dynamics. We use the vector and matrix technique to the N-dimensional Euler equations, to construct the following Cartesian vector form solutions
u = b(t) + A(t)x.
One advantage of this approach is that the Euler equations with Coriolis force can be solved both theoretically and algebraically, which can be accomplished by constructing appropriate matrices A(t) and vector b(t). We can obtain the new exact solutions using the required matrices A(t) and vector b(t). As exact solutions for the compressible Euler equations are rare, the new exact solutions are valuable for the verification of the corresponding computational methods. Copyright © 2021 Published by Elsevier B.V. on behalf of The Physical Society of the Republic of China (Taiwan).