arXiv 论文重写 OpenAI Navier-Stokes 有限时间爆破证明的剖面构造部分
Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder
有人把 OpenAI 那篇 Navier-Stokes 爆破论文里最难懂的部分重写成了可读版本，还引入了新线性模型解释内核构造，数学爱好者可以看看。
该论文以更易读的方式重写了 OpenAI 手稿《Finite Time Blowup for Navier-Stokes》中的剖面构造部分，作者认为 OpenAI 的工作是 Navier-Stokes 千禧年大奖问题上的重要进展。论文构造的剖面光滑且轴对称，代入 Navier-Stokes 方程后，残差由一个散度形式项和一个在固定相似扇区内于 1-t 处无穷阶消失的余项组成。应力与径向剪切满足可容许锥条件，且应力无需很小。作者还引入一个新的线性模型来更清晰地解释内核构造，振荡脉冲的残差修正将放在第二部分处理。
Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder
This paper gives a readable and accessible version of the profile-construction part of OpenAI's manuscript "Finite Time Blowup for Navier-Stokes". We regard OpenAI's work as a major advance on the Navier-Stokes Millennium Prize Problem. The profiles are smooth and axi-symmetric. Inserting them into the Navier-Stokes equations gives a residual consisting of a divergence-form term and a remainder vanishing to infinite order in $1-t$ on fixed similarity sectors. The associated stress and radial shear satisfy the admissible cone condition. The stress need not be small. We introduce a new linear model that provides a clearer explanation of the inner core construction. The cancellation by oscillatory pulses will be treated in the companion paper "Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses".
