1. DICATAM, University of Brescia, Via Valotti 9, 25133 Brescia, Italy;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;3. Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China
Abstract:
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) 20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.