Un th�or�me d'existence de solutions d'un probl�me de shallow water

Orenga, Pierre

doi:10.1007/bf00375155

Cited by 64 publications

(41 citation statements)

References 4 publications

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“…Several choices have been considered in the literature for the viscous term 14 : in Ref. 17, the author chose the laplacian and obtained an existence result, but this system is not energetically consistent. In Ref.…”

Section: U(t X): Velocitymentioning

confidence: 99%

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An Energetically Consistent Viscous Sedimentation Model

Zabsonré

Lucas

Fernández-Nieto

2009

Math. Models Methods Appl. Sci.

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Section: U(t X): Velocitymentioning

confidence: 99%

“…21 but, in this article, the ShallowWater system is taken as in Ref. 17, that is to say the viscous term is a laplacian. Here, we couple Eq.…”

Section: Model Coming From Those Studied Abovementioning

confidence: 99%

An Energetically Consistent Viscous Sedimentation Model

Zabsonré

Lucas

Fernández-Nieto

2009

Math. Models Methods Appl. Sci.

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“…It is frequently used in several applications, see for example [1], [21], [22] or [26]. It is obtained by integration of the NavierStokes equations in the vertical direction and by assuming…”

Section: Other Evolution Modelsmentioning

confidence: 99%

“…where σ = ρ (ν(∇u+ t ∇u)−p Id) is the stress tensor and ρ and ρ air are respectively the water and air densities, see [19] p. 22. The friction coefficient c s depends on waves height.…”

Section: Introductionmentioning

confidence: 99%

On the Effect of Friction on Wind Driven Shallow Lakes

Bresch

Simon

2001

J. math. fluid mech.

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We investigate the steady motion of a liquid in a lake, modeled as a thin domain. We assume the motion is governed by Navier-Stokes equations, while a Robin-type traction condition, and a friction condition is prescribed at the surface and at the bottom, respectively. We also take into account Coriolis forces. We derive an asymptotic model as the aspect ratio δ = depth/width of the domain goes to 0. When the Reynolds number is not too large, this is mathematically justified and the three-dimensional limit velocity is given in terms of wind, bathymetry, depth and of a two-dimensional potential. Numerical simulation is carried out and the influence of traction condition reading is experienced. Mathematics Subject Classification (2000). 35Q30, 35B40, 76D05.

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“…In [14] and [25], the authors prove the existence of global weak solution of a bi-layer Shallow-Water model without any friction term but with a diffusion term of the form ν∆u. This analysis uses the method developed by Orenga in [24] and the system is energetically consistent only for small enough initial data. Others works concerning the existence of global weak solution of a bi-layer Shallow-Water using the preceding method can also find in [11] and [23].…”

Section: Introductionmentioning

confidence: 99%