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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)2011-2029
Journal / PublicationDiscrete and Continuous Dynamical Systems - Series S
Issue number6
Publication statusPublished - Dec 2016


The global existence of weak solutions to the three space dimensional Prandtl equations is studied under some constraint on its structure. This is a continuation of our recent study on the local existence of classical solutions with the same structure condition. It reveals the sufficiency of the monotonicity condition on one component of the tangential velocity field and the favorable condition on pressure in the same direction that leads to global existence of weak solutions. This generalizes the result obtained by Xin-Zhang [14] on the two-dimensional Prandtl equations to the three-dimensional setting.

Research Area(s)

  • 3D Prandtl equations, Favorable pressure, Global existence, Monotonic velocity field, Weak solutions