Nonlinear stability of the Guderley imploding shock wave in radial symmetry
Abstract
Nonlinear stability of the Guderley imploding shock under radial perturbations is established for 3D compressible Euler equations via weighted estimates and computer-assisted verification.
We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range 1<γleq5{3}. The perturbed solutions develop an asymptotically self-similar implosion in finite time. Our result allows perturbations with small, nonzero constant pressure in the quiescent region ahead of the shock. The proof combines weighted L^infty estimates along characteristics with a computer-assisted proof of stability inequalities for the Guderley profile.
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