On the delta-Primitive and Boussinesq Type Equations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Advances in Differential Equations Year : 2005

On the delta-Primitive and Boussinesq Type Equations

Madalina Petcu
  • Function : Author
  • PersonId : 842686
Antoine Rousseau
  • Function : Author
  • PersonId : 3416
  • IdHAL : aroussea

Abstract

In this article we consider the Primitive Equations without horizontal viscosity but with a mild vertical viscosity added in the hydrostatic equation, as in [13] and [16], which are the so-called δ−Primitive Equations. We prove that the problem is well posed in the sense of Hadamard in certain types of spaces. This means that we prove the finite-in-time existence, uniqueness and continuous dependence on data for appropriate solutions. The results given in the 3D periodic space easily extend to dimension 2. We also consider a Boussinesq type of equation, meaning that the mild vertical viscosity present in the hydrostatic equation is replaced by the time derivative of the vertical velocity. We prove the same type of results as for the δ−Primitive Equations; periodic boundary conditions are similarly considered.
Fichier principal
Vignette du fichier
PR05.pdf (433.95 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

inria-00172497 , version 1 (17-09-2007)

Identifiers

  • HAL Id : inria-00172497 , version 1

Cite

Madalina Petcu, Antoine Rousseau. On the delta-Primitive and Boussinesq Type Equations. Advances in Differential Equations, 2005, 10 (5), pp.579-599. ⟨inria-00172497⟩
99 View
112 Download

Share

Gmail Facebook Twitter LinkedIn More