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.
@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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