A COUNTEREXAMPLE RELATED TO THE NAVIER-STOKES PROBLEM
Keywords:
the Navier-Stokes problemDOI:
https://doi.org/10.17654/0972096023012Abstract
It is proved that the solution to the Navier-Stokes problem (NSP) in the whole space $\mathbb{R}^3$ does not exist if the smooth rapidly decaying data are not equal to zero identically. This solves the millennium problem concerning the NSP. It also proves that the NSP is contradictory.
Received: May 16, 2023
Accepted: June 20, 2023
References
T. Kato, Strong $L^p$-solutions of the Navier-Stokes equation in $mathbb{R}^m$, with applications to weak solutions, Math. Z. 187 (1984), 471-480.
L. Landau and E. Lifshitz, Fluid Mechanics, Pergamon Press, New York, 1964.
A. G. Ramm, The Navier-Stokes Problem, Morgan & Clay Publishers, 2021 (expanded second edition published by Springer in 2023).
A. G. Ramm, Navier-Stokes equations paradox, Reports on Math. Phys. (ROMP) 88(1) (2021), 41-45.
A. G. Ramm, Comments on the Navier-Stokes problem, Axioms 10 (2021), 95.
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