收缩多孔壁之间的自相似旋流：在OpenAI 2026受迫爆炸构造的相似变量中重新审视GD1998精确Navier-Stokes解
Self-similar swirl between contracting porous walls: the GD1998 exact Navier-Stokes solution revisited in the similarity variables of the OpenAI 2026 forced blow-up construction
- University of Maryland, College Park（马里兰大学帕克分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究在OpenAI 2026受迫爆炸的相似变量中重新审视GD1998精确旋流解，发现其无法直接转化，转而求解广义二维剖面问题，揭示对称破缺与临界折叠，并指出该机制在实际流动中不可达。
AI中文摘要：
OpenAI于2026年9月发布的受迫Navier-Stokes方程有限时间爆炸构造（OpenAI 2026）以各向异性相似变量中的轴对称旋流核心为对象。其几何形状与Gumerov和Duraiswami于1998年（GD1998）发现的旋转多孔圆柱之间的精确稳态旋流相同。我们发现GD1998边值问题无法转化为该相似变量，其推广形式是一个在固定相似半径的多孔壁之间的二维剖面问题，关于径向变量X为二阶，关于类时轴向变量η为一阶。我们通过带固定压力基准的张量Chebyshev配点法、复步长Newton法和弧长延拓求解该问题，并以三种方式验证，同时扫描径向Reynolds数、壁面旋流和对称破缺数据。当入流低于9时，解为单一光滑分支；高于该值时，对称分支在临界旋流F*=0.41V_0^2处折叠。Dirichlet轴问题没有分辨率稳定的解；核心必须是来自轴的Cauchy问题。其矩恒等式无法由关于分割面对称的核心满足：核心是轴向贯穿流，正如其作者所选择的那样；非对称核心满足这些恒等式的误差为0.2%。锥条件即带轴向剪切的Rayleigh准则，要求半径量级为10^20。动态重标度表明，在弱入流下该剖面为吸引子，在折叠附近为鞍结点；在中等入流和强旋流下，谱在轴向分辨率下不收敛，问题留待开放。真实流体会先发生空化（水）或激波（空气）；GD1998腔体被提议作为实验装置。未发现任何迹象表明该机制可在计算或构建的流动中实现；受迫定理及本研究使实践中的无受迫方程保持原状。代码、测试和日志随论文附上。
英文摘要：
The finite-time blow-up construction for the forced Navier-Stokes equations released by OpenAI in Sep. 2026 (OpenAI 2026) has as its object an axisymmetric swirl core in anisotropic similarity variables. Its geometry is that of an exact steady swirl between rotating porous cylinders found by Gumerov and Duraiswami in 1998 (GD1998). We find that the GD1998 boundary value problem does not recast into the similarity variables and that its generalization is a two-dimensional profile problem between porous walls held at fixed similarity radii, second order in the radial variable X and first order in the time-like axial variable $η$. We solve it by tensor Chebyshev collocation with a pinned pressure gauge, complex-step Newton and arclength continuation, verify it three ways, and sweep the radial Reynolds number, the wall swirl and a symmetry-breaking datum. Below inflow 9 the solution is one smooth branch; above it the symmetric branch folds at a critical swirl $F^*=0.41V_0^2$. The Dirichlet axis problem has no resolution-stable solution; the core must be a Cauchy problem from the axis. Its moment identities cannot be met by a core symmetric about the dividing plane: the core is an axial through-flow, as its authors chose it; a non-symmetric core meets them to 0.2%. The cone condition is Rayleigh's criterion with axial shear and requires radii of order $10^{20}$. Dynamic rescaling shows the profile to be an attractor at weak inflow and toward the fold, a saddle-node; at moderate inflow and strong swirl the spectrum does not converge in the axial resolution and is left open. A real fluid cavitates (water) or shocks (air) first; the GD1998 chamber is proposed as the experiment. Nothing found suggests the mechanism is reachable in a flow one computes or builds; the forced theorem, and this study, leave the unforced equations of practice as they were. Code, tests and log accompany the paper.
