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oseen semigroup

Journal of the Institute of Mathematics of Jussieu (1)

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ON LOCAL ENERGY DECAY ESTIMATE OF THE OSEEN SEMIGROUP IN TWO DIMENSIONS AND ITS APPLICATION
Part of
- Incompressible viscous fluids
- Partial differential equations
Yasunori Maekawa
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 3 / May 2021

Published online by Cambridge University Press:

01 July 2019, pp. 859-891

Print publication:

May 2021
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We study the temporal decay estimate of the Oseen semigroup in a two-dimensional exterior domain. We establish the local energy decay estimate with a suitable dependence on the small translation speed, which is a significant improvement of Hishida’s result in 2016. As an application, we prove the $L^{q}$-$L^{r}$ estimates of the Oseen semigroup uniformly in the small translation speed.