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  • Séminaire Laurent Schwartz — EDP et applications
  • Year 2011-2012
  • Talk no. 2
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Global in Time Stability of Steady Shocks in Nozzles
Jeffrey Rauch1; Chunjing Xie1; Zhouping Xin2
1 Department of Mathematics University of Michigan 530 Church Street Ann Arbor, MI 48109 USA
2 The Institute of Mathematical Sciences and department of mathematics The Chinese University of Hong Kong Hong Kong
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 2, 11 p.
  • Abstract

We prove global dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. One of the key improvements compared with previous results is that we assume neither the smallness of the slope of the nozzle nor the weakness of the shock strength. A key ingredient of the proof are the derivation a exponentially decaying energy estimates for a linearized problem.

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DOI: 10.5802/slsedp.2
Author's affiliations:
Jeffrey Rauch 1; Chunjing Xie 1; Zhouping Xin 2

1 Department of Mathematics University of Michigan 530 Church Street Ann Arbor, MI 48109 USA
2 The Institute of Mathematical Sciences and department of mathematics The Chinese University of Hong Kong Hong Kong
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@article{SLSEDP_2011-2012____A2_0,
     author = {Jeffrey Rauch and Chunjing Xie and Zhouping Xin},
     title = {Global in {Time} {Stability} of {Steady} {Shocks} in {Nozzles}},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:2},
     pages = {1--11},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2011-2012},
     doi = {10.5802/slsedp.2},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.2/}
}
TY  - JOUR
AU  - Jeffrey Rauch
AU  - Chunjing Xie
AU  - Zhouping Xin
TI  - Global in Time Stability of Steady Shocks in Nozzles
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:2
PY  - 2011-2012
SP  - 1
EP  - 11
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.2/
DO  - 10.5802/slsedp.2
LA  - en
ID  - SLSEDP_2011-2012____A2_0
ER  - 
%0 Journal Article
%A Jeffrey Rauch
%A Chunjing Xie
%A Zhouping Xin
%T Global in Time Stability of Steady Shocks in Nozzles
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:2
%D 2011-2012
%P 1-11
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.2/
%R 10.5802/slsedp.2
%G en
%F SLSEDP_2011-2012____A2_0
Jeffrey Rauch; Chunjing Xie; Zhouping Xin. Global in Time Stability of Steady Shocks in Nozzles. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 2, 11 p. doi : 10.5802/slsedp.2. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.2/
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