The concepts of well-posedness and stability in different function spaces for the 1D linearized Euler equations (Q1725179)

Summary: This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts ``perturbation,'' ``small perturbation,'' ``solution of the propagation problem,'' and ``small solution, that is, solution close to zero,'' which are specific for each function space.