Global well-posedness of $z$-weak solutions to the primitive equations without vertical diffusivity

Jinkai Li South China Normal University Guozhi Yuan South China Normal University

Analysis of PDEs mathscidoc:2108.03004

2021.7
In this paper, we consider the initial boundary value problem in a cylindrical domain to the three dimensional primitive equations with full eddy viscosity in the momentum equations but with only horizontal eddy diffusivity in the temperature equation. Global well-posedness of $z$-weak solution is established for any such initial datum that itself and its vertical derivative belong to $L^2$. This not only extends the results in \cite{Cao5} from the spatially periodic case to general cylindrical domains but also weakens the regularity assumptions on the initial data which are required to be $H^2$ there.
Primitive equations, global well-posedness, $z$-weak solutions, without vertical diffusivity.
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@inproceedings{jinkai2021global,
  title={Global well-posedness of $z$-weak solutions to the primitive equations without vertical diffusivity},
  author={Jinkai Li, and Guozhi Yuan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210824232325637238868},
  year={2021},
}
Jinkai Li, and Guozhi Yuan. Global well-posedness of $z$-weak solutions to the primitive equations without vertical diffusivity. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210824232325637238868.
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