In this paper, we present an analysis of the Kelvin-Helmholtz instability in two-dimensional ideal compressible elastic flows, providing a rigorous confirmation that weak elasticity has a destabilizing effect on the Kelvin-Helmholtz instability. There are two critical velocities, \(U_{\text {low}}\) and \(U_{\text {upp}}\) , where \(U_{\text {low}}\) and \(U_{\text {upp}}\) represent the lower and upper critical velocities, respectively. We demonstrate that when the magnitude of the rectilinear solutions satisfies \(U_{\text {low}}+c\epsilon _{0}\le |\dot{v}^{+}_{1}| \le U_{\text {upp}}-c\epsilon _{0}\) , the linear and nonlinear ill-posedness of the piecewise smooth solutions of the Kelvin-Helmholtz problem for two-dimensional ideal compressible elastic flows is established uniformly with respect to the background velocity in the interval \([U_{\text {low}}+c\epsilon _{0}, U_{\text {upp}}-c\epsilon _{0}]\) , where c is the sound speed and \(\epsilon _{0}\) is some small enough positive constant.
