On the Two-Dimensional Hydrostatic Navier--Stokes Equations

Bresch, Didier; Kazhikhov, A. V.; Lemoine, J M

doi:10.1137/s0036141003422242

Cited by 49 publications

(44 citation statements)

References 10 publications

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“…The result proved in Petcu, Temam and Wirosoetisno [15] is the following; see also Bresch, Kazhikhov and Lemoine [1] and Temam and Ziane [22]. To access this journal online: http://www.birkhauser.ch…”

Section: R Temammentioning

confidence: 79%

Some Mathematical Aspects of Geophysical Fluid Dynamic Equations

Témam

2003

Milan Journal of Mathematics

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In this article we present the classical primitive equations of the ocean, and we summarize a number of results concerning the wellposedness of the associated boundary and initial value problems: some of the results have been known for about ten years or so, and some of the results correspond to very recent results which were proven during the past two years or so. Some indications are also given about the problems of the atmosphere, which are similar, and the coupled ocean and atmosphere.

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Section: R Temammentioning

confidence: 79%

Some Mathematical Aspects of Geophysical Fluid Dynamic Equations

Témam

2003

Milan Journal of Mathematics

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“…[6][7][8], the authors studied the hydrostatic Navier-Stokes equations which correspond to the primitive equations where the density is assumed to be constant. Guillén-González, et al [8] obtained global existence results of strong solution, by assuming the data are small enough.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [7], the authors considered the two-dimensional hydrostatic Navier-Stokes equations with Dirichlet boundary conditions at the bottom, assuming a basin with a strictly positive depth. They obtained the existence and uniqueness of the global strong solution and the exponential decay in time of the energy.…”

Section: Introductionmentioning

confidence: 99%

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On two-dimensional large-scale primitive equations in oceanic dynamics (I)

黄代文

郭柏灵

2007

Appl Math Mech

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The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.

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“…We mention here the similar works of Bresch, Kazhikhov and Lemoine [2] and of Ziane [13], who consider different boundary conditions and do not consider the higher regularity results needed in [9]; see also [11]. For the non-dimensional form of the PEs, we refer here for example to [4], [8], and [12] but a substantial amount of literature is available on this subject.…”

mentioning

confidence: 99%

Existence and regularity results for the primitive equations in two space dimensions

Petcu¹,

Témam²,

Wirosoetisno³

2004

Communications on Pure &Amp; Applied Analysis

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Abstract. Our aim in this article is to present some existence, uniqueness and regularity results for the Primitive Equations of the ocean in space dimension two with periodic boundary conditions. We prove the existence of weak solutions for the PEs, the existence and uniqueness of strong solutions and the existence of more regular solutions, up to C ∞ regularity.1. Introduction. The objective of this article is to derive various results of existence and regularity of solutions for the Primitive Equations of the ocean (PEs) in two space dimensions. These results, besides their intrinsic interest, are needed in [9] which is another motivation of this work.We consider the PEs in their nondimensional form (see Section 5) :

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On the Two-Dimensional Hydrostatic Navier--Stokes Equations

Cited by 49 publications

References 10 publications

Some Mathematical Aspects of Geophysical Fluid Dynamic Equations

Some Mathematical Aspects of Geophysical Fluid Dynamic Equations

On two-dimensional large-scale primitive equations in oceanic dynamics (I)

Existence and regularity results for the primitive equations in two space dimensions

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