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

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.

Keywords

• non-isentropic fluids
• euler equations
• coriolis force
• linear-damping symmetric and anti-symmetric matrices
• curve integration
• cartesian vector form solutions