L² theory for the operator Δ+(κ×χ)・∇　in exterior domains

• HISHIDA T.

  Department of Applied Mathematics, Faculty of Engineering, NiigataUniversity

抄録

In exterior domains of R^3, we consider the differential operator △+(k×x)・▽ with Dirichlet boundary condition, where k stands for the angular velocity of a rotating obstacle. We show, among others, a certain smoothing property together with estimates near t=0 of the generated semigroup (it is not an analytic one) in the space L^2. The result is not trivial because the coefficient k×x is unbounded at infinity. The proof is mainly based on a cut-off technique. The equation ∂_<iu>=△u+(k×x)・▽u can be taken as a model problem for a linearized form of the Navier-Stokes equations in a domain exterior to a rotating obstacle. This paper is a step toward an analysis of the Navier-Stokes flow in such a domain.

収録刊行物

• Nihonkai Mathematical Journal

  Nihonkai Mathematical Journal 11 (2), 103-135, 2000

  新潟大学

詳細情報

• CRID: 1570854176770163840
• NII論文ID: 110000069825
• NII書誌ID: AA10800960
• ISSN: 13419951
• Web Site: http://hdl.handle.net/10191/5655
• Web Site: https://niigata-u.repo.nii.ac.jp/records/2188
• 本文言語コード: en
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