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Nonlinear stability of the Guderley imploding shock wave in radial symmetry
PDE & Applied Mathematics| Speaker: | Giorgio Cialdea, Courant NYU |
| Location: | Zoom |
| Start time: | Thu, Oct 29 2026, 4:10PM |
Description
We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range $1<\gamma≤\frac53$. 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.