Consider the small perturbations u and Uc to a motionless gas. Let u and U = Uc + U, where Uis a constant density value. Show that when linearized, the isothermal Euler equations reduce to Analyze the...

Consider the small perturbations u and Uc to a motionless gas. Let u and U = Uc + U, where Uis a constant density value. Show that when linearized, the isothermal Euler equations reduce to

Analyze the characteristics of the Jacobian matrix of the above equations. Show also that the combination of the above two equations yields

where a is the speed of sound,