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On Weighted Estimates for the Stokes Flows, with Application to the Navier–Stokes Equations

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Abstract

Weighted estimates on the Stokes flows are given by means of the Stokes solution formula in the half space, which can be regarded as a complement and improvement on the previous known results. There are two main difficulties: in weighted cases, usual \(L^q-L^r\) estimates for the Stokes flows do not work any more, and the projection operator becomes unbounded possibly. Finally, as an application, employing these weighted estimates on the Stokes solution, we establish some weighted decay results for the Navier–Stokes flows.

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Acknowledgements

The author expresses sincere thanks to the anonymous referees for many helpful suggestions and kind comments. This work was supported by NSFC under Grant No. 11471322; and NSFC-NRF under Grant No. 11611540331; supported by Key Laboratory of RCSDS, CAS (No. 2008DP173182); supported by Youth Innovation Promotion Association of the Chinese Academy of Sciences.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Pigong Han

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Pigong Han

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The author declares that the work described in the above article complied with the ethical standards, has also not been submitted elsewhere for publication, in whole or in part. Moreover, there is no financial or competing interests to disclose in relation to this work.

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Communicated by D. Chae

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Han, P. On Weighted Estimates for the Stokes Flows, with Application to the Navier–Stokes Equations. J. Math. Fluid Mech. 20, 1155–1172 (2018). https://doi.org/10.1007/s00021-018-0360-y

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