Real variable methods in harmonic analysis and Navier-Stokes equations. (English) Zbl 1486.35327
Rassias, Michael Th. (ed.), Harmonic analysis and applications. Cham: Springer. Springer Optim. Appl. 168, 243-277 (2021).
The question of existence and smoothness of solutions to the Navier-Stokes equations is one of the seven Millenium Prize Problems proposed in 2000 by the Clay Mathematics Institute of Cambridge, Massachusetts. The question discussed in this paper is, in author’s words, “to which extent harmonic analysis is used or should be used to study the Clay question on Navier-Stokes equations. Or, more generally, to discuss the Navier-Stokes equations on the whole space \(\mathbb{R}^3\) in various functional settings while using tools from real-variable methods in harmanic analysis.”
For the entire collection see [Zbl 1470.42003].
For the entire collection see [Zbl 1470.42003].
Reviewer: Gheorghe Moroşanu (Cluj-Napoca)
MSC:
| 35Q30 | Navier-Stokes equations |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 42B37 | Harmonic analysis and PDEs |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
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