We study the regularity of semihyperbolic patches of self-similar solutions near sonic lines to a Riemann problem for the two-dimensional (2-D) Euler system. As a result, it is verified that there exists a global solution in the semihyperbolic patch up to the sonic boundary and that the sonic boundary has C1-regularity. The study of the semihyperbolic patches of solutions for the Euler system was initiated by Li and Zheng [Arch. Rational Mech. Anal., 201 (2011), pp. 1069-1096]. This type of solution appears in the transonic flow over an airfoil and Guderley reflection and is common in the numerical configurations of 2-D Riemann problems.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics