Rigorous linear radial stability of the Guderley imploding shock

Prove linear stability of the Guderley imploding shock wave under radial perturbations, thereby establishing the rigorous linear result that remains unresolved beyond the numerical and perturbative evidence cited for this problem.

Background

The paper discusses earlier numerical investigations of the Guderley imploding shock, particularly Morawetz’s analysis of the linearized operator and later perturbative work by Chen, Zhang, and Panarella. These studies suggested decay of non-symmetry modes under radial perturbations but did not provide a rigorous proof.

The present paper proves nonlinear radial stability and allows a small constant nonzero pressure in the interior, but the explicitly identified rigorous linear-stability problem is distinct and is not resolved as an independent result.