On isomorphism for the space of solenoidal vector fields and its application to the Stokes problem

Maekawa, Yasunori; Miura, Hideyuki

Hokkaido University Preprint Series in Mathematics, 2015, 1076, 1-15

Permalink : https://doi.org/10.14943/84220

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DOI	https://doi.org/10.14943/84220
URI	https://hdl.handle.net/2115/69880
タイトル	On isomorphism for the space of solenoidal vector fields and its application to the Stokes problem
著者	著者名 Maekawa, Yasunori
著者	著者名 Miura, Hideyuki
言語	英語
キーワード	Solenoidal vector fields
	incompressible flows
	Helmholtz projection
	reduction argument
	factorization of elliptic operators
発行日	2015-08-27
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1076
ページ	1-15
抄録	We consider the space of solenoidal vector fields in an unbounded domain Ω ⊂ Rn whose boundary is given as a Lipschitz graph. It is shown that, under suitable functional setting, the space of solenoidal vector fields is isomorphic to the n − 1 product space of the space of scalar functions. As an application, we introduce a natural and systematic reduction of the equations describing the motion of incompressible flows. This gives a new perspective of the derivation of Ukai’s solution formula for the Stokes equations in the half space, and provides a key step for the generalization of Ukai’s approach to the Stokes semigroup in the case of the curved boundary.
資源タイプ	紀要論文
出版タイプ	Version of Record