Communications in Information and Systems

Volume 13 (2013)

Number 1

Special Issue in Honor of Marshall Slemrod: Part 1 of 4

Global regularity for an inviscid three-dimensional slow limiting ocean dynamics model

Pages: 97 – 122

DOI: https://dx.doi.org/10.4310/CIS.2013.v13.n1.a4

Authors

Chongsheng Cao (Department of Mathematics, Florida International University, Miami, Fl., U.S.A.)

Aseel Farhat (Department of Mathematics, Indiana University, Bloomington, In., U.S.A.)

Edriss S. Titi (Dept. of Mathematics and Dept. of Mechanical and Aero-space Engineering, University of California at Irvine, U.S.A.; Dept. of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel)

Abstract

We establish, for smooth enough initial data, the global well-posedness (existence, uniqueness and continuous dependence on initial data) of solutions, for an inviscid three-dimensional slow limiting ocean dynamics model. This model was derived as a strong rotation limit of the rotating and stratified Boussinesq equations with periodic boundary conditions. To establish our results, we utilize the tools developed for investigating the two-dimensional incompressible Euler equations and linear transport equations. Using a weaker formulation of the model, we also show the global existence and uniqueness of solutions, for less regular initial data.

Keywords

three-dimensional Boussinesq equations, slowdynamics, ocean model, global regularity

2010 Mathematics Subject Classification

35Q35, 76B03, 86A10

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Published 28 May 2014