Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data
Abstract
We investigate large time existence of solutions of the Navier-Stokes-Boussinesq equations with spatially almost periodic large data when the density stratification is sufficiently large. In 1996, Kimura and Herring \cite{KH} examined numerical simulations to show a stabilizing effect due to the stratification. They observed scattered two-dimensional pancake-shaped vortex patches lying almost in the horizontal plane. Our result is a mathematical justification of the presence of such two-dimensional pancakes. To show the existence of solutions for large times, we use -norm of amplitudes. Existence for large times is then proven using techniques of fast singular oscillating limits and bootstrapping argument from a global-in-time unique solution of the system of limit equations.
Keywords
Cite
@article{arxiv.1109.6088,
title = {Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data},
author = {Slim Ibrahim and Tsuyoshi Yoneda},
journal= {arXiv preprint arXiv:1109.6088},
year = {2011}
}