Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Toshiaki Hishida
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Toshiaki Hishida: Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

Mathematics, 2021, vol. 9, issue 8, 1-19

Abstract: In this expository paper, we study L q - L r decay estimates of the evolution operator generated by a perturbed Stokes system in n -dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space R n together with the energy relation imply the desired estimates in exterior domains provided n ? 3 .

Keywords: decay estimate; evolution operator; perturbed Stokes system; exterior domain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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