Lq$L^q$‐weak solutions to the time‐dependent 3D Oseen system: Decay estimates

This article deals with Lq$L^q$‐weak solutions to the 3D time‐dependent Oseen system. This type of solution is defined in terms of the velocity only. It is shown that the velocity may be represented by a sum of integrals none of which involves the pressure and without a surface integral of the spati...

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Bibliographic Details
Published in:Mathematische Nachrichten 2023-01, Vol.296 (1), p.164-195
Main Author: Deuring, Paul
Format: Article
Language:English
Subjects:
Boundary conditions
Decay
integral representation
Mathematics
Oseen system
spatial decay
Time dependence
weak solutions
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Summary:This article deals with Lq$L^q$‐weak solutions to the 3D time‐dependent Oseen system. This type of solution is defined in terms of the velocity only. It is shown that the velocity may be represented by a sum of integrals none of which involves the pressure and without a surface integral of the spatial gradient of the velocity. On the basis of this representation formula, an estimate of the spatial decay of the velocity and its spatial gradient is derived. No boundary conditions have to be imposed for these results.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202000272