We establish the well-posedness in Gevrey function space with optimal class of regularity 2 for the three-dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system. This shows that the three-dimensional instabilities in the system leading to ill-posedness are not worse than the two-dimensional ones. © 2021 Wiley Periodicals LLC.

中文翻译：

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没有结构假设的 3D Prandtl 方程的 Gevrey 函数空间中的适定性

我们在没有任何结构假设的情况下为三维普朗特系统建立了具有最优规律类 2 的 Gevrey 函数空间中的适定性。该证明以一种新颖的方式将系统中的新取消与一些旧思想结合起来，以克服系统中导数丢失的困难。这表明系统中导致不适定性的三维不稳定性并不比二维不稳定性差。© 2021 威利期刊有限责任公司。