2024-03-29T10:26:09Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697922022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116LONG-TIME SOLVABILITY OF THE NAVIER-STOKES-BOUSSINESQ EQUATIONS WITH ALMOST PERIODIC INITIAL LARGE DATAIbrahim, SlimYoneda, Tsuyoshiopen access410We 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.Department of Mathematics, Hokkaido University2011-09-12engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84132http://hdl.handle.net/2115/6979210.14943/84132Hokkaido University Preprint Series in Mathematics985116https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69792/1/pre985.pdfapplication/pdf316.76 KB2011-09-12