Can smooth three-dimensional incompressible Navier–Stokes flow develop a finite-time singularity?

details For viscosity $\nu>0$, consider the three-dimensional incompressible Navier–Stokes equations

on $\mathbb R^3$ or the periodic three-torus, with smooth divergence-free initial velocity $u_0$ of finite energy. Prove that every such initial datum generates a global smooth solution, or construct admissible smooth initial data for which a singularity forms in finite time. A numerical simulation of apparent blow-up, or a proof for a restricted symmetry class, is not a resolution of the full problem.

Why are most people in the world poor? How can we change it?

平衡三进制是什么，如果我要用它做计算机，应该如何存储和计算，请结合图示说明。

根据【华尔街之狼】自动生成一张收藏版史诗叙事海报：巨大的【李治达】侧脸剪影作为外轮廓，剪影内部自动生长出最契合该主题的完整世界观、标志性场景、角色关系、象征符号、关键建筑、生物、道具与氛围。整体不是普通拼贴，而是高级的剪影轮廓填充式叙事合成，带有双重曝光式联想，但更偏电影海报与梦幻水彩插画融合风格；柔和空气透视，轻雾化过渡，纸张颗粒，边缘飞白与刷痕，大面积留白，版式克制高级，安静、宏大、神圣、怀旧、诗意、传说感。风格、色彩、场景、材质全部根据主题自动适配，所有元素必须强绑定主题，一眼识别，不要杂乱，不要硬拼贴，不要模板化背景，不要廉价奇幻素材。 李治达的参考图片：

帮我把这个女生变成赛博朋克风