Existence and stability of perturbed transonic shocks for compressible steady potential flows

✍ Scribed by Eun Heui Kim

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 435 KB
• Volume: 69
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.07.058

✦ Synopsis

We establish an existence theorem for perturbed transonic steady potential flows where the boundary of the subsonic region consists of a transonic shock and thus the governing equation becomes a free boundary problem. We establish gradient estimates and use the fixed point theorem of Caristi's, which does not require a compactness of the map, to establish the existence result. We provide new techniques to handle the gradients and show that the flow is strictly elliptic inside of the subsonic region.