On multi-dimensional linear stability of planar shock waves for Chaplygin gases

This paper is concerned with linear stability of planar shock waves in two dimensional compressible isentropic Euler equations for Chaplygin gases. The main feature is that the characteristic fields are always linearly degenerate. By establishing energy estimates, especially high-order energy estimates, in terms of the nonhomogeneous terms and variable coefficients, we prove that planar shock waves are linearly stable.