2022-05-24T15:34:57Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697922018-04-25T23:44:11Zhdl_2115_45007hdl_2115_116LONG-TIME SOLVABILITY OF THE NAVIER-STOKES-BOUSSINESQ EQUATIONS WITH ALMOST PERIODIC INITIAL LARGE DATAIbrahim, SlimYoneda, Tsuyoshi410We 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.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69792info:doi/10.14943/84132https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69792/1/pre985.pdfHokkaido University Preprint Series in Mathematics9851162011-09-12engpublisher