Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit

Maekawa, Yasunori

Hokkaido University Preprint Series in Mathematics, 2011, 992, 1-29

Permalink : https://doi.org/10.14943/84139

このアイテムのアクセス数:810件（2026-04-06 20:57 集計）

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アクセス権	open access
DOI	https://doi.org/10.14943/84139
URI	https://hdl.handle.net/2115/69798
タイトル	Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit
著者	著者名 Maekawa, Yasunori
言語	英語
キーワード	Navier-Stokes equations
	Vorticity equations
	No-slip boundary conditions
	Inviscid limit
発行日	2011-12-26
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	992
ページ	1-29
抄録	We consider the Navier-Stokes equations for viscous incompressible flows in the half plane under the no-slip boundary condition. In this paper we first establish a solution formula for the vorticity equations through the appropriate vorticity formulation. The formula is then applied to establish the asymptotic expansion of vorticity fields at ! 0 that holds at least up to the time c 1=3, where is the viscosity coefficient and c is a constant. As a consequence, we get a natural sufficient condition on the initial data for the vorticity to blow up in the inviscid limit, together with explicit estimates.
資源タイプ	紀要論文
出版タイプ	Version of Record