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Abstract and Applied Analysis
Volume 2014, Article ID 872548, 10 pages
http://dx.doi.org/10.1155/2014/872548
Research Article

The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

1Department of Computer Science, West University of Timisoara, Boulevard Vasile Pârvan 4, 300223 Timisoara, Romania
2Department of Physics, West University of Timisoara, Boulevard Vasile Pârvan 4, 300223 Timisoara, Romania

Received 30 August 2013; Revised 8 December 2013; Accepted 15 December 2013; Published 12 January 2014

Academic Editor: Abdullah Alotaibi

Copyright © 2014 Stefan Balint and Agneta M. Balint. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.