Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data

Details Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data

2011-09-28

arxiv.org/abs/1109.6088v1

Mathematics

Analysis of PDEs

Scientific paper

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 $\ell^1$-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.

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