发表机构
New York University（纽约大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了三维可压缩欧拉方程中Guderley内爆激波在径向扰动下的非线性稳定性，采用加权L∞估计与计算机辅助证明相结合的方法，允许激波前存在小常数压力扰动。
AI 中文摘要
我们证明了在绝热范围$1<\gamma\leq\frac{5}{3}$内，三维可压缩欧拉方程中Guderley内爆激波在径向扰动下的非线性稳定性。扰动解在有限时间内发展出渐近自相似的聚爆过程。我们的结果允许激波前方静止区域存在小的非零常数压力扰动。证明结合了沿特征线的加权$L^\infty$估计与对Guderley剖面稳定性不等式的计算机辅助证明。
英文摘要
We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range $1<γ\leq\frac{5}{3}$. 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.
