AI 中文总结
该研究针对二维各向同性Navier-Stokes方程，证明单方向耗散可保证自然能量水平下弱解的能量等式，克服方向正则性缺失的困难，进而推导弱-强唯一性原理。
AI 中文摘要
在二维情形下，我们证明在一个空间方向上的耗散足以在自然能量水平下对每个弱解成立能量等式，尤其不会出现异常的能量损失或产生。主要困难在于缺失的方向正则性阻碍了常规的自检验论证，我们通过两个观察克服这一障碍：压力通过方向Riesz变换估计是平方可积的，且正则性较低的分量仍是重整化解。作为能量刚性的应用，我们推导出弱-强唯一性原理。
英文摘要
In two dimensions, we show that dissipation in one spatial direction is sufficient to enforce the energy equality for every weak solution at the natural energy level. In particular, neither anomalous energy loss nor creation can occur. The main difficulty is that the missing directional regularity prevents the usual self-testing argument. We overcome this obstruction through two observations: The pressure is square-integrable by a directional Riesz-transform estimate, and the less regular component is still a renormalized solution. As an application of energy rigidity, we derive a weak-strong uniqueness principle.
