Global existence of weak solutions to the three-dimensional Prandtl equations with A special structure

摘要

The global existence of weak solutions to the three space dimensional Prandtlequations is studied under some constraint on its structure. This is acontinuation of our recent study on the local existence of classical solutionswith the same structure condition. It reveals the sufficiency of themonotonicity condition on one component of the tangential velocity field andthe favorable condition on pressure in the same direction that leads to globalexistence of weak solutions. This generalizes the result obtained by Xin-Zhangon the two-dimensional Prandtl equations to the three-dimensional setting.