2023-03-26T21:26:33Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698152022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A Mathematical clue to the separation phenomena on the two-dimensional Navier-Stokes equationYoneda, Tsuyoshiopen accessNavier-Stokers equationseparation phenomenapressure analysis410In general, before separating from a boundary, the flow moves toward reverse direction near the boundary against the laminar flow direction. Here in this paper, a clue of such reverse flow phenomena (in the mathematical sense) is observed. More precisely, the non-stationary two-dimensional Navier-Stokes equation with an initial datum having a parallel laminar flow (we de ne it rigorously in the paper) is considered. We show that the direction of the material di erentiation is opposite to the initial flow direction and e ect of the material di erentiation (inducing the reverse flow) becomes bigger when the curvature of the boundary becomes bigger. We also show that the parallel laminar flow cannot be a stationary Navier-Stokes flow near a portion of the boundary with nonzero curvature.Department of Mathematics, Hokkaido University2012-06-08engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84156http://hdl.handle.net/2115/6981510.14943/84156Hokkaido University Preprint Series in Mathematics1010112https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69815/1/pre1010.pdfapplication/pdf269.5 KB2012-06-08