Transonic Shocks in Multidimensional Divergent Nozzles

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We establish existence, uniqueness and stability of transonic shocks for a steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equation. In the process, we obtain unique solvability for a class of transport equations with velocity fields of weak regularity (non-Lipschitz), an infinite dimensional weak implicit mapping theorem which does not require continuous Fr,chet differentiability, and regularity theory for a class of elliptic partial differential equations with discontinuous oblique boundary conditions.
Publisher
SPRINGER
Issue Date
2011-09
Language
English
Article Type
Article
Citation

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.201, no.3, pp.777 - 840

ISSN
0003-9527
DOI
10.1007/s00205-011-0424-0
URI
http://hdl.handle.net/10203/280623
Appears in Collection
MA-Journal Papers(저널논문)
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