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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Analyticity up to the boundary for the Stokes and the Navier-Stokes systems


Authors: Guher Camliyurt, Igor Kukavica and Vlad Vicol
Journal: Trans. Amer. Math. Soc. 373 (2020), 3375-3422
MSC (2010): Primary 35Q35; Secondary 76D05
DOI: https://doi.org/10.1090/tran/7990
Published electronically: February 19, 2020
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Abstract: We consider the Stokes and Navier-Stokes equations in a bounded domain with analytic boundary. We present a direct, robust, energy-type approach for establishing the instantaneous gain of space-time analyticity of the solution from any Sobolev smooth initial datum, with analyticity radius which is uniform up to the curved boundary.


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Additional Information

Guher Camliyurt
Affiliation: Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540
Email: camliyurt@math.ias.edu

Igor Kukavica
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: kukavica@usc.edu

Vlad Vicol
Affiliation: Department of Mathematics, Courant Institute of Mathematical Sciences, New York, New York 10012
Email: vicol@cims.nyu.edu

DOI: https://doi.org/10.1090/tran/7990
Keywords: Real analyticity, Gevrey regularity, bounded domain, Stokes equation.
Received by editor(s): January 25, 2019
Received by editor(s) in revised form: August 27, 2019
Published electronically: February 19, 2020
Additional Notes: The first author was supported in part by the Ambrose Monell Foundation
The second author was supported in part by the NSF grants DMS-1615239 and DMS-1907992
The third author was supported in part by the NSF grant DMS-1911413.
Article copyright: © Copyright 2020 American Mathematical Society