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

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Title: On isomorphism for the space of solenoidal vector fields and its application to the Stokes problem
Authors: Maekawa, Yasunori Browse this author
Miura, Hideyuki Browse this author
Keywords: Solenoidal vector fields
incompressible flows
Helmholtz projection
reduction argument
factorization of elliptic operators
Issue Date: 27-Aug-2015
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1076
Start Page: 1
End Page: 15
Abstract: 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69880
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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