On the relation between very weak and Leray–Hopf solutions to Navier–Stokes equations
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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.References
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Additional Information
- Giovanni P. Galdi
- Affiliation: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
- MR Author ID: 70660
- Email: galdi@pitt.edu
- 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
- © Copyright 2019 American Mathematical Society
- 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
- MathSciNet review: 4021094