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Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space

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Abstract

We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in \({\mathbb {R}}^n_+ \times (0,T)\). We obtain new estimates of solutions including pressure in terms of mixed anisotropic Sobolev spaces. As an application, some anisotropic Sobolev estimates are presented for weak solutions of the Navier–Stokes equations in a half-space in dimension three.

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Acknowledgements

T.-K. Chang’s work was partially supported by NRF20151009350 and K. Kang’s work was partially supported by NRF-2012R1A1A2001373 and NRF-2014R1A2A1A11051161.

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  1. Department of Mathematics, Yonsei University, Seoul, Republic of Korea

    Tongkeun Chang & Kyungkeun Kang

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  1. Tongkeun Chang
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  2. Kyungkeun Kang
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Correspondence to Tongkeun Chang.

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Chang, T., Kang, K. Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space. Ann Univ Ferrara 64, 47–82 (2018). https://doi.org/10.1007/s11565-017-0287-x

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