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

Analysis of PDEs 2015-09-15 v1

Abstract

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 on the two-dimensional Prandtl equations to the three-dimensional setting.

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Cite

@article{arxiv.1509.03856,
  title  = {Global existence of weak solutions to the three-dimensional Prandtl equations with A special structure},
  author = {Cheng-Jie Liu and Ya-Guang Wang and Tong Yang},
  journal= {arXiv preprint arXiv:1509.03856},
  year   = {2015}
}

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20 pages