Mathematical study of the Equatorial Shallow Water and Navier-Stokes equations
type: Dataset
description: This thesis is divided into two parts. In the first one, we are interested in the Equatorial Shallow Water equations which modelize the behaviour of shallow homogeneous fluids in the equatorial zone in case of large rotation of the Earth. Thanks to these hypotheses, using the Navier-Stokes equations, we get a penalized system. The penalization parameter is called " and takes into account the smallness hypotheses. Studying the penalization term, we exhibit a formal limit system when the parameter " tends to zero. Finally, we prove the convergence of the filtered solutions toward the solution of the limit system. In the second part, we exhibit a class of initial data which generate a global solution of the Navier-Stokes equations in R3. These equations are well-posed in R2 but in R3 we need, for example, to add a su cient smallness condition on the initial data. When the inital data spectrum is near the horizontal plane then we will prove that it generates a global solution to the Navier-Stokes equations. Moreover, we establish that, under some hypotheses, the perturbation of an initial data generating a global solution, by these data with quasi- horizontal spectrum, also generates a global solution.
identifier: NNT: 2011PA066538
issued: 2026-05-11T00:59:56.281534
language: fr
modified: 2026-05-11T00:59:56.281539
contact point: Organization
  fn: CCSD
keyword: donnees-bien-preparees
keyword: donnees-mal-preparees
keyword: equatorial-shallow-wate
keyword: equatorial-shallow-water
keyword: fi-ltering-method
keyword: fi-ltrage
keyword: global-wellposedness
keyword: globalite
keyword: ill-prepared-initial-data
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-dsmathematics-mathdynamical-systems-mathds
keyword: navier-stokes
keyword: penalisation-antisymetrique
keyword: saint-venant
keyword: skew-symmetric-penalization
keyword: symmetric-system
keyword: systeme-symetrique
keyword: theses
keyword: well-prepared-initial-data
landing page: https://theses.hal.science/tel-00825556

Mathematical study of the Equatorial Shallow Water and Navier-Stokes equations
type: Distribution
format: HTML
issued: 2026-05-11T00:59:56.312846
modified: 2026-05-11T00:59:56.261889
access URL: https://theses.hal.science/tel-00825556

test_moissonnage_selune
type: Agent