On the energy equality for distributional solutions to Navier–Stokes equations
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- by Giovanni P. Galdi PDF
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Abstract:
A classical result of J.-L. Lions asserts that if a solution to the Navier–Stokes equations is such that (i) it is in the Leray–Hopf class and (ii) belongs to $L^4(0,T;L^4)$, then it must satisfy the energy equality in the time interval $[0,T]$. In this note we show that assumption (i) is not necessary.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): October 16, 2017
- Received by editor(s) in revised form: October 21, 2017, May 13, 2018, and May 17, 2018
- Published electronically: October 12, 2018
- Additional Notes: This work was supported in part by NSF DMS Grant-1614011.
- Communicated by: Catherine Sulem
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 785-792
- MSC (2010): Primary 76D05, 35Q30, 76D03; Secondary 76D07
- DOI: https://doi.org/10.1090/proc/14256
- MathSciNet review: 3894916