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Volume 9
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10.3390/math9080841
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Article

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

by
Toshiaki Hishida
Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
Mathematics 2021, 9(8), 841; https://doi.org/10.3390/math9080841
Submission received: 22 February 2021 / Revised: 26 March 2021 / Accepted: 7 April 2021 / Published: 12 April 2021
(This article belongs to the Special Issue Maximal Regularity, Stability Estimates and Mathematical Fluid Dynamics)
Versions Notes

Abstract

In this expository paper, we study Lq-Lr 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 Rn 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 decay estimate; evolution operator; perturbed Stokes system; exterior domain

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MDPI and ACS Style

Hishida, T. Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains. Mathematics 2021, 9, 841. https://doi.org/10.3390/math9080841

AMA Style

Hishida T. Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains. Mathematics. 2021; 9(8):841. https://doi.org/10.3390/math9080841

Chicago/Turabian Style

Hishida, Toshiaki. 2021. "Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains" Mathematics 9, no. 8: 841. https://doi.org/10.3390/math9080841

APA Style

Hishida, T. (2021). Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains. Mathematics, 9(8), 841. https://doi.org/10.3390/math9080841

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