Sonic-supersonic solutions for the two-dimensional pseudo-steady full Euler equations

Yanbo Hu, ,Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036, China, Tong Li, ,Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States
2019 Kinetic and Related Models  
This paper is focused on the existence of classical sonic-supersonic solutions near sonic curves for the two-dimensional pseudo-steady full Euler equations in gas dynamics. By introducing a novel set of change variables and using the idea of characteristic decomposition, the Euler system is transformed into a new system which displays a transparent singularity-regularity structure. With a choice of weighted metric space, we establish the local existence of smooth solutions for the new system by
more » ... r the new system by the fixed-point method. Finally, we obtain a local classical solution for the pseudo-steady full Euler equations by converting the solution from the partial hodograph variables to the original variables. 2010 Mathematics Subject Classification. 35L65, 35L80, 76H05.
doi:10.3934/krm.2019046 fatcat:hiwzzfa4nbhoxhs7eplmts2rui