On the stability of two-dimensional nonisentropic elastic vortex sheets

<p style="text-indent:20px;">We are concerned with the stability of vortex sheet solutions for two-dimensional nonisentropic compressible flows in elastodynamics. This is a nonlinear free boundary hyperbolic problem characteristic discontinuities, which has extra difficulties when considering effect entropy. The addition thermal to system makes analysis Lopatinski<inline-formula><tex-math id="M1">\begin{document}$ \breve{{\mathrm{i}}} $\end{document}</tex-math></inline-formula> determinant extremely complicated. Our results twofold. First, through qualitative roots id="M2">\begin{document}$ linearized problem, we find that sheets weakly stable some supersonic and subsonic regions. Second, under small perturbation entropy, can be adapted from previous isentropic elastic [<xref ref-type="bibr" rid="b6">6</xref>] by applying Nash-Moser iteration. two confirm strong stabilization sheets. In particular, our conditions linear (1) ensure regime as well one always persist any given configuration, (2) show how condition changes fluctuation. existence bubble, phenomenon not observed Euler flow, specially due elasticity.</p>