Long-Time Solvability of the Navier-Stokes-Boussinesq Equations with Almost Periodic Initial Large Data
Vol. 20 (2013), No. 1, Page 1–25.
Ibrahim, Slim ; Yoneda, Tsuyoshi
Long-Time Solvability of the Navier-Stokes-Boussinesq Equations with Almost Periodic Initial Large Data
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Abstract:
We investigate long time existence of solutions of the Navier-Stokes-Boussinesq equations with spatially almost periodic\break large data when the density stratification parameter is sufficiently large. In 1996, Kimura and Herring \cite{KH} examined numerical simulations to show a stabilizing effect due to the large stratification. They observed scattered two-dimensional pancake-shaped vortex patches lying almost in the horizontal plane. Our result gives a mathematical foundation of the presence of such two-dimensional pancakes.
Keywords: Navier-Stokes equation, Boussinesq approximation, almost periodic functions.
Mathematics Subject Classification (2010): Primary 76D50; Secondary 42B05.
Mathematical Reviews Number: MR3112085
Received: 2012-05-07
