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Partial and spectral-viscosity models for geophysical flows

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Abstract

Two models based on the hydrostatic primitive equations are proposed. The first model is the primitive equations with partial viscosity only, and is oriented towards large-scale wave structures in the ocean and atmosphere. The second model is the viscous primitive equations with spectral eddy viscosity, and is oriented towards turbulent geophysical flows. For both models, the existence and uniqueness of global strong solutions are established. For the second model, the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established.

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Authors and Affiliations

  1. Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306, USA

    Qingshan Chen & Max Gunzburger

  2. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    Xiaoming Wang

Authors
  1. Qingshan Chen
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  2. Max Gunzburger
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  3. Xiaoming Wang
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Correspondence to Qingshan Chen.

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Dedicated to Professor Roger Temam on the Occasion of his 70th Birthday

The first and second authors supported by the US Department of Energy grant (No. DE-SC0002624) as part of the “Climate Modeling: Simulating Climate at Regional Scale” program, and the third author supported by the National Science Foundation (No. DMS0606671, DMS1008852).

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Chen, Q., Gunzburger, M. & Wang, X. Partial and spectral-viscosity models for geophysical flows. Chin. Ann. Math. Ser. B 31, 579–606 (2010). https://doi.org/10.1007/s11401-010-0607-2

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