Global in Time Stability of Steady Shocks in Nozzles

Rauch, Jeffrey; Xie, Chunjing; Xin, Zhouping

doi:10.5802/slsedp.2

Rauch, Jeffrey ¹ ; Xie, Chunjing ¹ ; Xin, Zhouping 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

Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 2, 11 p.

Résumé

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.

DOI : 10.5802/slsedp.2

Affiliations des auteurs :

Rauch, Jeffrey ¹ ; Xie, Chunjing ¹ ; Xin, Zhouping ²

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     title = {Global in {Time} {Stability} of {Steady} {Shocks} in {Nozzles}},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
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     pages = {1--11},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
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     doi = {10.5802/slsedp.2},
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Rauch, Jeffrey; Xie, Chunjing; Xin, Zhouping. Global in Time Stability of Steady Shocks in Nozzles. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 2, 11 p. doi : 10.5802/slsedp.2. http://www.numdam.org/articles/10.5802/slsedp.2/

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