Functiones et Approximatio Commentarii Mathematici

Renormalized estimates for solutions to the Navier-Stokes equation

Jens Frehse and Maria Specovius-Neugebauer

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For weak solutions to the three-dimensional Navier-Stokes equations the interior regularity problem for the renormalized velocity $u(1+|u|^2)^{-\alpha/2}$ and pressure $p(1+|u|^2)^{-\beta/2}$ is investigated. If a velocity component is locally semibounded and $\nabla u$ slightly more regular than suitable weak solutions the regularity estimates for the renormalized velocity are improved. Furthermore, estimates for the negative part of a renormalized pressure are presented.

Article information

Funct. Approx. Comment. Math., Volume 40, Number 1 (2009), 11-32.

First available in Project Euclid: 30 March 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76D05: Navier-Stokes equations [See also 35Q30]
Secondary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]

Navier-Stokes equations interior regularity Morrey conditions


Frehse, Jens; Specovius-Neugebauer, Maria. Renormalized estimates for solutions to the Navier-Stokes equation. Funct. Approx. Comment. Math. 40 (2009), no. 1, 11--32. doi:10.7169/facm/1238418795.

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