关于三维纳维-斯托克斯方程复数解爆破的计算机模拟
Computer simulations for the blow-up of complex solutions of the 3-d Navier-Stokes equations
AI总结：
研究通过计算机模拟分析三维纳维-斯托克斯方程复数解的爆破机制，发现能量和涡量在物理空间的少数点附近集中，而其他区域保持平静。
摘要：
我们通过计算机模拟研究了整个空间中三维纳维-斯托克斯方程的一类复数解，根据李和辛纳的观点，这些解在有限时间呈现爆破（奇点）。计算机结果允许对爆破机制进行详细研究，并显示了解在爆破时间附近的行为特征，例如能量和涡量在物理空间的少数点附近集中，而在该区域之外，'流体'保持'平静'。
英文摘要：
We present a study by computer simulations of a class of complex-valued solutions of the three-dimensional Navier-Stokes equations in the whole space, which, according to Li and Sinai, present a blow-up (singularity) at a finite time. The computer results allow a detailed study of the blow-up mechanism, and show interesting features of the behavior of the solutions near the blow-up time, such as the concentration of energy and enstrophy in a small region around a few points of physical space, while outside this region the "fluid" remains "quiet".
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