Geodesic
A note on the generalized energy inequality in the Navier-Stokes equations
Applications of Mathematics, Tome 48 (2003) no. 6, pp. 537-545.

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We prove that there exists a suitable weak solution of the Navier-Stokes equation, which satisfies the generalized energy inequality for every nonnegative test function. This improves the famous result on existence of a suitable weak solution which satisfies this inequality for smooth nonnegative test functions with compact support in the space-time.
DOI : 10.1023/B:APOM.0000024492.23444.29
Classification : 35Q30, 35Q35, 76D03, 76D05
Keywords: Navier-Stokes equations; suitable weak solution; generalized energy inequality 
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Kučera, Petr; Skalák, Zdeněk. A note on the generalized energy inequality in the Navier-Stokes equations. Applications of Mathematics, Tome 48 (2003) no. 6, pp. 537-545. doi : 10.1023/B:APOM.0000024492.23444.29. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024492.23444.29/

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