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We establish the well-posedness in Gevrey function space with optimal classof regularity 2 for the three dimensional Prandtl system without any structuralassumption. The proof combines in a novel way a new cancellation in the systemwith some of the old ideas to overcome the difficulty of the loss ofderivatives in the system.This shows that the three dimensional instabilitiesin the system leading to ill-posedness are not worse than the two dimensionalones.

Well-posedness in Gevrey function space for 3D Prandtl equations without Structural Assumption