Existence and uniqueness analysis of a detached shock problem for the potential flow
Date
2011ISSN
0362-546XSource
Nonlinear Analysis, Theory, Methods and ApplicationsVolume
74Issue
3Pages
705-720Google Scholar check
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We study a problem for two-dimensional steady potential and isentropic Euler equations in a bounded domain, where an artificial detached shock interacts with a wedge. Using the stream function, we obtain a free boundary problem for the subsonic state and the detached artificial shock curve and we prove that such configuration admits a unique solution in certain weighted Hlder spaces. The proof is based on various Hlder and Schauder estimates for second-order elliptic equations and fixed point theorems. Moreover, we pose an energy principle and remark that the physical attached shock is the minimizer of the energy functional. © 2010 Elsevier Ltd. All rights reserved.