LONG-TIME SOLVABILITY OF THE NAVIER-STOKES-BOUSSINESQ EQUATIONS WITH ALMOST PERIODIC INITIAL LARGE DATA

Ibrahim, Slim; Yoneda, Tsuyoshi

Hokkaido University Preprint Series in Mathematics, 2011, 985, 1-16

Permalink : https://doi.org/10.14943/84132

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DOI	https://doi.org/10.14943/84132
URI	https://hdl.handle.net/2115/69792
タイトル	LONG-TIME SOLVABILITY OF THE NAVIER-STOKES-BOUSSINESQ EQUATIONS WITH ALMOST PERIODIC INITIAL LARGE DATA
著者	著者名 Ibrahim, Slim
著者	著者名 Yoneda, Tsuyoshi
言語	英語
発行日	2011-09-12
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	985
ページ	1-16
抄録	We investigate large time existence of solutions of the Navier-Stokes-Boussinesq equations with spatially almost periodic large data when the density strati cation is su - ciently large. In 1996, Kimura and Herring [16] examined numerical simulations to show a stabilizing e ect due to the strati cation. They observed scattered two-dimensional pancake- shaped vortex patches lying almost in the horizontal plane. Our result is a mathematical justi cation of the presence of such two-dimensional pancakes. To show the existence of solutions for large times, we use `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.
資源タイプ	紀要論文
出版タイプ	Version of Record