Abstract
<p style="text-indent:20px;">We construct a supersonic-sonic smooth patch solution for the two dimensional steady Euler equations in gas dynamics. This patch is extracted from the Frankl problem in the study of transonic flow with local supersonic bubble over an airfoil. Based on the methodology of characteristic decompositions, we establish the global existence and regularity of solutions in a partial hodograph coordinate system in terms of angle variables. The original problem is solved by transforming the solution in the partial hodograph plane back to that in the physical plane. Moreover, the uniform regularity of the solution and the regularity of an associated sonic curve are also verified.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
General Medicine,Applied Mathematics,Analysis
Reference29 articles.
1. J. Barros-Neto and I. M. Gelfand, Fundamental solutions for the Tricomi operator, Ⅰ, Ⅱ, Ⅲ, Duke Math. J., 98 (1999), 465–483; 111 (2002), 561–584; 128 (2005), 119–140.
2. L. Bers, On the continuation of a potential gas flow across the sonic line, Tech. Notes Nat. Adv. Comm. Aeronaut., No. 2058, 1950.
3. G. Q. Chen, C. Dafermos, M. Slemrod, D. H. Wang.On two-dimensional sonic-subsonic flow, Commun. Math. Phys., 271 (2007), 635-637.
4. G. Q. Chen, F. M. Huang, T. Wang.Subsonic-sonic limit of approximate solutions to multidimensional steady Euler equations, Arch. Ration. Mech. Anal., 219 (2016), 719-740.
5. S. X. Chen.Generalized Tricomi problem for a quasilinear mixed type equation, Chin. Ann. Math. Ser. B, 30 (2009), 527-538.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献