The intuition is false, and fluid mecanic prouves that. The theory of instability shows that the solutions can be very different.

In this project, I have studied the Kuramoto-Sivashinski equation which an illustration of the instabilities of the fluid mecanic.

The Karamoto-Sivashinsky equation (KSE) is a one-dimensional partial derivative equation. It's most usual form is :

Firstly, I have theoriticaly studied the stability of this equation, then as the theoretical study become to hard, I have begin the numerical simulation of the KSE. The final part of this report contain the main result I have obtained.