Asymptotics and lower bound for the lifespan of solutions to the Primitive Equations

Frédéric Charve

Asymptotics and lower bound for the lifespan of solutions to the Primitive Equations

Analysis of PDEs 2014-11-26 v1

Authors: Frédéric Charve

Abstract

This article generalizes a previous work in which the author obtained a large lower bound for the lifespan of the solutions to the Primitive Equations, and proved convergence to the 3D quasi-geostrophic system for general and ill-prepared (possibly blowing-up) initial data that are regularization of vortex patches related to the potential velocity. These results were obtained for a very particular case when the kinematic viscosity $\nu$ is equal to the heat diffusivity $\nu '$ , turning the diffusion operator into the classical Laplacian. Obtaining the same results without this assumption is much more difficult as it involves a non-local diffusion operator. The key to the main result is a family of a priori estimates for the 3D-QG system that we obtained in a companion paper.

Keywords

Primitive Equations lifespan lower bound quasi-geostrophic system non-local diffusion operator a priori estimates

Cite

@article{arxiv.1411.6859,
  title  = {Asymptotics and lower bound for the lifespan of solutions to the Primitive Equations},
  author = {Frédéric Charve},
  journal= {arXiv preprint arXiv:1411.6859},
  year   = {2014}
}

Related papers

View all related →