Global in Time Stability of Steady Shocks in Nozzles

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

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-11
  • ISSN: 2266-0607

Abstract

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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.

How to cite

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Rauch, Jeffrey, Xie, Chunjing, and Xin, Zhouping. "Global in Time Stability of Steady Shocks in Nozzles." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-11. <http://eudml.org/doc/251175>.

@article{Rauch2011-2012,
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.},
affiliation = {Department of Mathematics University of Michigan 530 Church Street Ann Arbor, MI 48109 USA; Department of Mathematics University of Michigan 530 Church Street Ann Arbor, MI 48109 USA; The Institute of Mathematical Sciences and department of mathematics The Chinese University of Hong Kong Hong Kong},
author = {Rauch, Jeffrey, Xie, Chunjing, Xin, Zhouping},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {transonic shock solutions; inviscid compressible isentropic Euler equations},
language = {eng},
pages = {1-11},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Global in Time Stability of Steady Shocks in Nozzles},
url = {http://eudml.org/doc/251175},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Rauch, Jeffrey
AU - Xie, Chunjing
AU - Xin, Zhouping
TI - Global in Time Stability of Steady Shocks in Nozzles
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 11
AB - 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.
LA - eng
KW - transonic shock solutions; inviscid compressible isentropic Euler equations
UR - http://eudml.org/doc/251175
ER -

References

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