Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 340, Issue -, Pages 83-110Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2022.08.020
Keywords
Stokes; Navier-Stokes flow; Strong solution; Decay rate; Besov space; Triebel-Lizorkin space
Categories
Funding
- Australian Research Council [DP190100970]
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This study investigates the non-stationary Navier-Stokes equation in the upper half space of Rn and proves the decay estimates of the strong solution and its derivatives in the Besov and Triebel-Lizorkin spaces. It is the first time that such decay estimates have been established on these spaces, extending the known results and providing new estimates.
Consider the non-stationary Navier-Stokes equation in the upper half space of Rn. We prove the decay estimates of the strong solution and its derivatives in the setting of Besov and Triebel-Lizorkin spaces. This is the first time that the decay estimates of solutions to the non-stationary Navier-Stokes equations on Besov and Triebel-Lizorkin spaces are established. Our results not only extend the known results from Hardy spaces to Besov and Triebel-Lizorkin spaces but also imply new estimates on Sobolev spaces and give better decay estimates on Hardy spaces. (c) 2022 Elsevier Inc. All rights reserved.
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