ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 64, Issue 1, pp 47–82 | Cite as

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.

Keywords

Stokes system Navier–Stokes equations Anisotropic Sobolev space 

Mathematics Subject Classification

35K51 76D07 

Notes

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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Copyright information

© Università degli Studi di Ferrara 2017

Authors and Affiliations

  1. 1.Department of MathematicsYonsei UniversitySeoulRepublic of Korea

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