2024-06-20T03:43:19Z
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oai:niigata-u.repo.nii.ac.jp:00002188
2022-12-15T03:34:59Z
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L² theory for the operator Δ+(κ×χ)・∇ in exterior domains
L² theory for the operator Δ+(κ×χ)・∇ in exterior domains
Hishida, Toshiaki
7418
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.
journal article
新潟大学
2000
application/pdf
Nihonkai Mathematical Journal
2
11
103
135
Nihonkai Mathematical Journal
AA10800960
13419951
https://niigata-u.repo.nii.ac.jp/record/2188/files/5_0008.pdf
eng