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The Inviscid Three Dimensional Quasi-Geostrophic System on Bounded Domains

Abstract

We present a formal derivation of the inviscid three dimensional quasi-geostrophic system (QG) from primitive equations on a bounded, cylindrical domain. A key point in the derivation is the treatment of the lateral boundary and the resulting boundary conditions it imposes on solutions. To our knowledge, these boundary conditions are new and differentiate our model from closely related models which have been the object of recent study. These boundary conditions are natural for a variational problem in a particular Hilbert space. We construct solutions and prove an elliptic regularity theorem corresponding to the variational problem, allowing us to show the existence of global weak solutions to QG.

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Acknowledgements

The Alexis F. Vasseur was partially funded by the NSF (Grant No. 1209420) during this work.

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Correspondence to Matthew D. Novack.

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Communicated by P. Constantin.

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Novack, M.D., Vasseur, A.F. The Inviscid Three Dimensional Quasi-Geostrophic System on Bounded Domains. Arch Rational Mech Anal 235, 973–1010 (2020). https://doi.org/10.1007/s00205-019-01437-x

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