2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221878This paper has been withdrawn by the author due to the fact that the negative sign of the exponent of $R$ in (2.20) is not allowed by the second inequality of (2.2), and thus the desired vanishing in (2.20) could not be obtained by this method.19 pagesAnalysis of PDEs35Q30, 35Q35, 76Dxx, 76BxxOn the Liouville theorem for the Navier-Stokes and the Euler equations in $\Bbb R^N$text