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Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces
Han, Pigong1,2
AbstractThere is a long standing problem on the nonstationary Navier-Stokes equations which pertains to how to characterize the L-1-time asymptotic expansion of the Navier-Stokes flows in the half space. Beyond a few partial results, new progress has not yet to be made on this open question. In this article, we give a confirmed answer to this problem; namely, a thorough characterization on L-1-summability is revealed. In order to prove this result, we need to avoid the unboundedness of the projection operator, which is overcome by treating an elliptic Neumann problem. Finally, using the weighted estimates on the heat kernel's convolution, we obtain the exact profile structure of the asymptotic expansion in L1(R+n). In addition, some crucial estimates on the fractional spatial derivatives of the non-stationary Stokes and Navier-Stokes flows are established for the first time, which allows for a better understanding of the L-1-decay problem.
WOS Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000443822500005
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Document Type期刊论文
Corresponding AuthorHan, Pigong
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Han, Pigong. Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2018,230(3):977-1015.
APA Han, Pigong.(2018).Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,230(3),977-1015.
MLA Han, Pigong."Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 230.3(2018):977-1015.
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