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Nonlinearity Volume 13 Number 3 Create an alert RSS this journal

Igor Kukavica 2000 Nonlinearity 13 639 doi:10.1088/0951-7715/13/3/307

A ladder inequality for the Navier-Stokes equation

Igor Kukavica

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Abstract References Cited By

We introduce a ladder inequality for L p norms of vorticity for the two- and three-dimensional Navier-Stokes equation. With its help, we improve existing pointwise estimates on the algebraic minimal scale in terms of the Grashof number and in terms of the vorticity magnitude. In particular, we prove that it can be bounded by

C( \nu t / ( 1+\sup_{0<\tau<t} \tau \Vert \omega(\tau)\Vert_{L^{\infty}} ) )^{1/2}

improving the corresponding estimate from Henshaw et al.


PACS

47.10.ad Navier-Stokes equations

02.30.Jr Partial differential equations

MSC

76D05 Navier-Stokes equations (See also 35Q30)

35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)

35K55 Nonlinear PDE of parabolic type

Subjects

Fluid dynamics

Mathematical physics

Dates

Issue 3 (May 2000)

Received 20 April 1999, in final form 24 November 1999



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