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2008 Uniform gradient bounds for the primitive equations of the ocean
Igor Kukavica, Mohammed Ziane
Differential Integral Equations 21(9-10): 837-849 (2008). DOI: 10.57262/die/1356038588


In this paper, we consider the 3D primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side and bottom boundaries. We provide an explicit upper bound for the $H^{1}$ norm of the solution. We prove that, after a finite time, this norm is less than a constant which depends only on the viscosity $\nu$, the force $f$, and the domain $\Omega$. This improves our previous result from [7] where we established the global existence of strong solutions with an argument which does not give such explicit rates.


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Igor Kukavica. Mohammed Ziane. "Uniform gradient bounds for the primitive equations of the ocean." Differential Integral Equations 21 (9-10) 837 - 849, 2008.


Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35346
MathSciNet: MR2483337
Digital Object Identifier: 10.57262/die/1356038588

Primary: 35Q35
Secondary: 35B45 , 35B65 , 76D03 , 76U05 , 86A05

Rights: Copyright © 2008 Khayyam Publishing, Inc.


Vol.21 • No. 9-10 • 2008
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