TY - JOUR
T1 - The regularity of semi-hyperbolic patches at sonic lines for the pressure gradient equation in gas dynamics
AU - Wang, Qin
AU - Zheng, Yuxi
PY - 2014
Y1 - 2014
N2 - We study the uniformregularity of semi-hyperbolic patches of self-similar solutions near sonic lines to a general Riemann problem for the pressure gradient equation. This type of solution, in which one family of characteristics starts on a sonic line and ends on a transonic shock wave, is common for the Riemann problems for the Euler system in two space dimensions. The global existence of smooth solutions was established in Song and Zheng [Disc. Cont. Dyna. Syst., 24 (2009),1365-1380], but the smoothness near the sonic lines is not clear. We establish that the smooth solutions are uniformly smooth up to their sonic boundaries, and that the sonic lines are C1 continuous.
AB - We study the uniformregularity of semi-hyperbolic patches of self-similar solutions near sonic lines to a general Riemann problem for the pressure gradient equation. This type of solution, in which one family of characteristics starts on a sonic line and ends on a transonic shock wave, is common for the Riemann problems for the Euler system in two space dimensions. The global existence of smooth solutions was established in Song and Zheng [Disc. Cont. Dyna. Syst., 24 (2009),1365-1380], but the smoothness near the sonic lines is not clear. We establish that the smooth solutions are uniformly smooth up to their sonic boundaries, and that the sonic lines are C1 continuous.
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U2 - 10.1512/iumj.2014.63.5244
DO - 10.1512/iumj.2014.63.5244
M3 - Article
AN - SCOPUS:84904472769
SN - 0022-2518
VL - 63
SP - 385
EP - 402
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
IS - 2
ER -