Abstract
In this paper, we show the unique existence of solutions to the nonstationary problem for the modified Oseen equation with rotating effect in Ω
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References
M. E. Bogovskiǐ, Solution of Some Vector Analysis Problems connected with Operators div and grad (Russian). Trudy Seminar S.L. Sobolev, No. 1, 80, Akademia Nauk SSR, Sibirskoe Otdelenie Matematiki, Nowosibirsk, 5–40 (1980)
Y. Enomoto and Y. Shibata, On the rate of decay of the Oseen semigroup in exterior domains and its application to Navier-Stokes equation. J. Math. Fluid Mech. 7, 339–367 (2005)
R. Farwig, An L q-analysis of viscous fluid flow past a rotating obstacle. Tôhoku Math. J. 58, 129–147 (2006)
R. Farwig, T. Hishida and D. Müller, L q-theory of a singular “winding” integral operator arising from fluid dynamics. Pacific. J. Math. 215, 297–312 (2004)
R. Farwig and J. Neustupa, On the Spectrum of an Oseen-type operator arising from flow past a rotating body. Integr. Equat. Operat. Theor. 62, 169–189 (2008)
R. Farwig and H. Sohr, Generalized resolvent estimates for the Stokes operator in bounded and unbounded domains. J. Math. Soc. Japan 46, 607–643 (1994)
D. Fujiwara and H. Morimoto, An L r -theory of the Helmholtz decomposition of vector fields. J. Fac. Sci. Univ. Tokyo, Sect. Math. 24, 685–700 (1977)
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol. I: Linear Steady Problems, Vol. II: Nonlinear Steady Problems. Springer Tracts in Nat. Ph. 38, 39, Springer Verlag, New York (1994) 2nd edition (1998)
G. P. Galdi and A. L. Silvestre, The steady motion of a Navier-Stokes liquid around a rigid body. Arch. Rational Mech. Anal. 184, 371–400 (2007).
G. P. Galdi and A. L. Silvestre, Further results on steady-state flow of a Navier-Stokes liquid around a rigid body, Existence of the wake. Kyoto Conference on the Navier-Stokes Equations and their applications, RIMS Kokyuroku Bessatsu B1, 127–143 (2007)
M. Geissert, H. Heck and M. Hieber, L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle. J. Reine Angew. Math. 596, 45–62 (2006)
M. Geissert, H. Heck and M. Hieber, On the equation div u = g and Bogovskii’s operator in Sobolev spaces of negative order. Operat. Theor. Advan. Appl. 168, 113–121 (2006)
T. Hishida and Y. Shibata, L p –L q estimate of the Stokes operator and Navier-Stokes flows in the exterior of a rotating obstacle. Arch. Rational Mech. Anal. 193, 339–421 (2009)
T. Kobayashi and Y. Shibata, On the Oseen equation in the three dimensional exterior domains. Math. Ann. 310, 1–45 (1998)
T. Miyakawa, On non-stationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J. 12, 115–140 (1982)
A. Noll and J. Saal, H ∞-calculus for the Stokes operator on L q -spaces. Math. Z. 244, 651–688 (2003)
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci. Springer-Verlag, New York, 44 (1983)
Y. Shibata, On the exterior initial boundary value problem for Navier-Stokes equations. Quartely Appl. Math. LVII(1), 117–155 (1999)
Y. Shibata, Time-global solutions of nonlinear evolution equations and their stability. Amer. Math. Soc. Transl. 211(2), 87–105 (2003)
Y. Shibata, On the Oseen semigroup with rotating effect. Functional Analysis and Evolution Equations, The Günter Lumer Volume, H. Amann et al (eds.), Birkhauser Verlag, Basel, 595–611 (2008)
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. North Holland, Amsterdam (1978)
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Shibata, Y. (2010). On a C 0 Semigroup Associated with a Modified Oseen Equation with Rotating Effect. In: Rannacher, R., Sequeira, A. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_29
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DOI: https://doi.org/10.1007/978-3-642-04068-9_29
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