An improved regularity result of semi-hyperbolic patch problems for the 2-D isentropic Euler equations

This paper investigates the regularity of a semi-hyperbolic patch problem arising from the Riemann problem for the 2-D isentropic Euler equations. We show that the solution is uniformly C1,16 up to the sonic curve and the sonic curve is C1,16, which improve the C1-regularity of Song et al. [20]. We introduce a novel set of change variables which allow us to establish higher regularity results based on the ideas of characteristic decomposition and the bootstrap method.