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.