Abstract
We give conditions for regularity of solutions of three dimensional incompressible Navier–Stokes equations based on the pressure and on structure functions.
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Berselli, L., Galdi, G.: Regularity criteria involving the pressure for the weak solutions to the Navier–Stokes equations. Proc. AMS 130(12), 3585–3595 (2002)
Cheskidov, A., Shvydkoy, R.: Volumetric theory of intermittency in fully developed turbulence arXiv:2203.11060 (2022)
Constantin, P.: Navier–Stokes equations and area of interfaces. Commun. Math. Phys. 129, 241–266 (1990)
Constantin, P.: Local formulas for the hydrodynamic pressure and applications. Russ. Math. Surv. 69, 395–418 (2014)
Constantin, P., Foias, C.: Navier–Stokes Equations. University of Chicago Press, Chicago (1988)
Escauriaza, L., Montaner, S.: Some remarks on the \(L^p\) regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28(1), 49–63 (2017). https://doi.org/10.4171/RLM/751
Foias, C.: personal communication, unpublished
Frisch, U.: Turbulence, the Legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge (1995)
Grujic, Z., Xu, L.: Asymptotic criticality of the Navier-Stokes regularity problem. arXiv:1911.00974v4 (2023)
Iyer, K.P., Sreenivasan, K.R., Yeung, P.K.: Scaling exponents saturate in three-dimensional isotropic turbulence. Phys. Rev. Fluids 5(5), 054605 (2020)
Seregin, G.: Lecture Notes on Regularity Theory for Navier–Stokes Equations. World Scientific Publishing, Singapore (2015)
Seregin, G., Sverak, V.: Regularity criteria for Navier–Stokes solutions. In: Giga, Y., Novotny, A. (eds.) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, pp. 829–867. Springer International Publishing, Berlin (2018)
Stein, E.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)
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Research partially supported by NSF Grant DMS-2106528.
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On the occasion of the centennial anniversary of O. A. Ladyzhenskaya.
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Constantin, P. Pressure, Intermittency, Singularity. J. Math. Fluid Mech. 25, 36 (2023). https://doi.org/10.1007/s00021-023-00779-7
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DOI: https://doi.org/10.1007/s00021-023-00779-7