Existence and Regularity Results for the Inviscid Primitive Equations with Lateral Periodicity

Existence and Regularity Results for the Inviscid Primitive Equations with Lateral Periodicity The article is devoted to prove the existence and regularity of the solutions of the 3 D inviscid Linearized Primitive Equations (LPEs) in a channel with lateral periodicity. This was assumed in a previous work (Hamouda et al. in Discret Contin Dyn Syst Ser S 6(2):401–422, 2013 ) which is concerned with the boundary layers generated by the corresponding viscous problem. Although the equations under investigation here are of hyperbolic type, the standard methods do not apply because of the specificity of the hyperbolic system. A set of non-local boundary conditions for the inviscid LPEs has to be imposed at the lateral boundary of the channel making thus the system well-posed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Existence and Regularity Results for the Inviscid Primitive Equations with Lateral Periodicity

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-016-9345-5
Publisher site
See Article on Publisher Site

Abstract

The article is devoted to prove the existence and regularity of the solutions of the 3 D inviscid Linearized Primitive Equations (LPEs) in a channel with lateral periodicity. This was assumed in a previous work (Hamouda et al. in Discret Contin Dyn Syst Ser S 6(2):401–422, 2013 ) which is concerned with the boundary layers generated by the corresponding viscous problem. Although the equations under investigation here are of hyperbolic type, the standard methods do not apply because of the specificity of the hyperbolic system. A set of non-local boundary conditions for the inviscid LPEs has to be imposed at the lateral boundary of the channel making thus the system well-posed.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2016

References

  • The barotropic mode for the primitive equations
    Chen, Q; Shiue, M-C; Temam, R
  • Boundary layers for the Navier-Stokes equation: the case of characteristic boundary
    Hamouda, M; Temam, R
  • Open boundary conditions for the primitive and Boussinesq equations
    Temam, R; Tribbia, J

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