三维可压缩欧拉流的不可避免激波形成
Inevitable shock formation for 3-D compressible Euler flows
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中文总结 AI 辅助
该研究证明三维无旋可压缩流的小紧支光滑扰动解必有限时间爆破，激波在最大柯西发展边界形成，其形成时间与辐射场分析预测的寿命一致。
中文摘要 AI 辅助
我们证明，三维无旋可压缩流中非真空常数状态的光滑、足够小、紧支扰动所产生的解，在无任何对称性假设或对初始数据的其他限制时，必然会在有限时间内爆破。此外，我们证明激波不可避免地在最大柯西发展的边界处形成，且在小数据渐近 regime 中，其形成时间与辐射场分析所预测的寿命一致。
英文摘要
We prove that solutions arising from smooth, sufficiently small, compactly supported perturbations of non-vacuum constant states in three-dimensional irrotational compressible flow must blow up in finite time, without any symmetry assumptions or other restrictions on the initial data. Moreover, we prove that shock inevitably forms at the boundary of the maximal Cauchy development, and that its formation time agrees, in the small-data asymptotic regime, with the lifespan predicted by the radiation-field analysis.
