Figure 1: The shock wave caused by a supersonic jet.
Originating authors are David Mumford and Christiane Rousseau.
Foreword: This vignette is more difficult than others. However, in a few pages, it tells you how to explain in simple terms one of the most difficult open problems at the beginning of the 21st century. The vignette contains enrichment material, that you can choose to read or skip. The editors of the Klein blog hesitated for a while posting this vignette. After testing it with teachers during two Klein workshops, who expressed that they enjoy being challenged by more difficult vignettes, they decided to test it on the blog. They are eager to hear your comments, and if some of you were motivated by this topic.
You have probably heard some planes breaking the sound barrier. What does that mean? It means that a shock wave in the atmosphere is created as in Figure 1. But what is a shock wave? Imagine heavy traffic on highways as a wave. A shock wave corresponds to collisions. To explain this, we develop our intuition with a 1D model: traffic on a one lane road at different speeds. You know that collisions could occur if drivers do not adjust their speed. The atmosphere is a fluid, and traffic is a rough model of 1D fluid which is convenient to develop our intuition. Under which conditions do shock waves or other singularities occur in fluids? A million dollar prize is offered for answering this question. This is what we are going to explain you.
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