approach of weak solutions to stationary rotating Oseen equations in exterior domains
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In this paper, the existence and uniqueness of a weak solution of a nonhomogeneous stationary Oseen flow around a rotating body in an exterior domain D was established and the localization procedure was combined with classical results in an appropriate bounded domain.Abstract:
We establish the existence and uniqueness of a weak solution of the three-dimensional nonhomogeneous stationary Oseen flow around a rotating body in an exterior domain D. We mainly use the localization procedure (see Kozono and Sohr (1991)) to combine our previous results (see Kracmar, Necasova, and Penel (2007, 2008)) with classical results in an appropriate bounded domain. We study the case of a nonintegrable right-hand side, where f is given in (W ―1,q (D)) 3 for certain values of q.read more
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Book ChapterDOI
Time-Periodic Solutions to the Navier-Stokes Equations
TL;DR: In this article, a maximal regularity framework for the Navier-Stokes system with time-periodic data is developed in a general L^q-setting, and the existence of a weak solution is proved without any restriction on the "size" of the data.
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A simple proof of Lq-estimates for the steady-state oseen and stokes equations in a rotating frame. parT I: Strong solutions
Giovanni P. Galdi,Mads Kyed +1 more
TL;DR: In this paper, a Navier-Stokes liquid rotating with angular velocity T e3 relative to some inertial relative to a fixed point is modeled as an Eulerian velocity and pressure term, where T ≥ 0 and T > 0 are dimensionless constants.
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Spectral analysis of a Stokes-type operator arising from flow around a rotating body
TL;DR: The spectrum of the Stokes operator with and without rotation effect for the whole space and exterior domains in $L^q$-spaces has been studied in this paper, where it has been shown that the spectrum as a set in the left complex half-plane does not change with the rotation.
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Linearized stationary incompressible flow around rotating and translating bodies: Asymptotic profile of the velocity gradient and decay estimate of the second derivatives of the velocity
TL;DR: In this article, the authors consider a system arising by linearization of a model for stationary viscous incompressible flow around a translating and rotating body and derive an asymptotic profile of the gradient of the velocity.
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An Lq-approach with generalized anisotropic weights of the weak solution of the Oseen flow around a rotating body in the whole space
TL;DR: In this paper, the stationary Oseen-type system for flow around a rotating body is studied in the whole three-dimensional space and the existence and uniqueness of a weak solution in weighted L q -spaces are established.
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Book
Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals
Elias M. Stein,Timothy S Murphy +1 more
TL;DR: In this article, the authors introduce the Heisenberg group and describe the Maximal Operators and Maximal Averages and Oscillatory Integral Integrals of the First and Second Kind.
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