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On the relation between very weak and Leray-Hopf solutions to Navier-Stokes equations


Author: Giovanni P. Galdi
Journal: Proc. Amer. Math. Soc. 147 (2019), 5349-5359
MSC (2010): Primary 76D05, 35Q30, 76D03; Secondary 76D07
DOI: https://doi.org/10.1090/proc/14764
Published electronically: September 20, 2019
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Abstract: We prove a general result that implies that very weak solutions to the Cauchy problem for the Navier-Stokes equations must be, in fact, Leray-Hopf solutions if only their initial data are (solenoidal) with finite kinetic energy.


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Additional Information

Giovanni P. Galdi
Affiliation: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Email: galdi@pitt.edu

DOI: https://doi.org/10.1090/proc/14764
Keywords: Navier--Stokes equations, very weak solutions, Leray--Hopf solutions, uniqueness, regularity
Received by editor(s): September 11, 2018
Received by editor(s) in revised form: February 27, 2019
Published electronically: September 20, 2019
Additional Notes: This work was supported in part by NSF DMS Grant-1614011
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society