TY - JOUR
T1 - Inviscid and viscous stationary waves of gas flow through contracting-expanding nozzles
AU - Hong, John M.
AU - Hsu, Cheng Hsiung
AU - Liu, Weishi
N1 - Funding Information:
E-mail addresses: [email protected] (J.M. Hong), [email protected] (C.-H. Hsu), [email protected] (W. Liu). 1 Partially supported by National Science Council of Taiwan. 2 Partially supported by National Science Council and NCTS of Taiwan. 3 Partially supported by National Science Foundation of USA Grant DMS-0807327 and University of Kansas GRF 2301264-003.
PY - 2010/1/1
Y1 - 2010/1/1
N2 - In this work we study steady states of one-dimensional viscous isentropic compressible flows through a contracting-expanding nozzle. Treating the viscosity coefficient as a singular parameter, the steady-state problem can be viewed as a singularly perturbed system. For a contracting-expanding nozzle, a complete classification of steady states is given and the existence of viscous profiles is established via the geometric singular perturbation theory. Particularly interesting is the existence of a maximal sub-to-super transonic wave and its role in the formation of other complicated transonic waves consisting of a sub-to-super portion.
AB - In this work we study steady states of one-dimensional viscous isentropic compressible flows through a contracting-expanding nozzle. Treating the viscosity coefficient as a singular parameter, the steady-state problem can be viewed as a singularly perturbed system. For a contracting-expanding nozzle, a complete classification of steady states is given and the existence of viscous profiles is established via the geometric singular perturbation theory. Particularly interesting is the existence of a maximal sub-to-super transonic wave and its role in the formation of other complicated transonic waves consisting of a sub-to-super portion.
KW - Contracting-expanding nozzles
KW - Gas flow
KW - Sub-to-super transonic waves
UR - http://www.scopus.com/inward/record.url?scp=70349777317&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2009.06.016
DO - 10.1016/j.jde.2009.06.016
M3 - 期刊論文
AN - SCOPUS:70349777317
SN - 0022-0396
VL - 248
SP - 50
EP - 76
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -