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St. Petersburg Mathematical Journal

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Sufficient conditions on Liouville type theorems for the 3D steady Navier-Stokes equations


Authors: G. Seregin and W. Wang
Original publication: Algebra i Analiz, tom 31 (2019), nomer 2.
Journal: St. Petersburg Math. J. 31 (2020), 387-393
MSC (2010): Primary 35Q30
DOI: https://doi.org/10.1090/spmj/1603
Published electronically: February 4, 2020
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Abstract: Our aim is to prove Liouville type theorems for the three dimensional steady-state Navier-Stokes equations provided the velocity field belongs to some Lorentz spaces. The corresponding statement contains several known results as a particular case.


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Additional Information

G. Seregin
Affiliation: Oxford University, United Kingdom; and St. Petersburg Branch Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
Email: seregin@maths.ox.ac.uk

W. Wang
Affiliation: Dalian University of Technology, China
Email: wendong@dlut.edu.cn

DOI: https://doi.org/10.1090/spmj/1603
Keywords: Liouville theorem, Navier--Stokes equations, Lorentz spaces
Received by editor(s): September 21, 2018
Published electronically: February 4, 2020
Additional Notes: The first author was supported by the grant RFBR no. 17-01-00099-a.
The second author was supported by NSFC under grant no. 11671067, “the Fundamental Research Funds for the Central Universities” and China Scholarship Council
Dedicated: Dedicated to Vladimir Maz′ya on the occasion of his 80th birthday
Article copyright: © Copyright 2020 American Mathematical Society