TY - JOUR
T1 - The uniqueness of transonic shocks in supersonic flow past a 2-D wedge
AU - Fang, Beixiang
AU - Xiang, Wei
PY - 2016/5/1
Y1 - 2016/5/1
N2 - We have proved the uniqueness of transonic shocks in steady supersonic flows past a slightly perturbed two-dimensional infinite wedge, under appropriate conditions on the downstream subsonic flows. We formulate it to a mathematical problem of the uniqueness of solutions of nonlinear partial differential equations of hyperbolic-elliptic mixed type with a free boundary. By working on several elliptic equations of physical quantities separately, we obtain a priori estimates of them, and then prove the uniqueness without assumptions on high regularity. Moreover, uniform estimates on the ellipticity and the positive lower bound of the speed are achieved under a geometrical condition on the wedge. The mathematical ideas and techniques developed here will also be useful for other related problems involving similar analytical difficulties.
AB - We have proved the uniqueness of transonic shocks in steady supersonic flows past a slightly perturbed two-dimensional infinite wedge, under appropriate conditions on the downstream subsonic flows. We formulate it to a mathematical problem of the uniqueness of solutions of nonlinear partial differential equations of hyperbolic-elliptic mixed type with a free boundary. By working on several elliptic equations of physical quantities separately, we obtain a priori estimates of them, and then prove the uniqueness without assumptions on high regularity. Moreover, uniform estimates on the ellipticity and the positive lower bound of the speed are achieved under a geometrical condition on the wedge. The mathematical ideas and techniques developed here will also be useful for other related problems involving similar analytical difficulties.
KW - 2-D wedge
KW - Potential flow equation
KW - Transonic shocks
KW - Uniqueness
UR - http://www.scopus.com/inward/record.url?scp=84959179040&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84959179040&origin=recordpage
U2 - 10.1016/j.jmaa.2015.11.067
DO - 10.1016/j.jmaa.2015.11.067
M3 - RGC 21 - Publication in refereed journal
VL - 437
SP - 194
EP - 213
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -