Lattice methods and the pressure field for solutions of the Navier-Stokes equations
- 1 January 1993
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 6 (1) , 79-91
- https://doi.org/10.1088/0951-7715/6/1/006
Abstract
As an alternative to removing the pressure field in regularity arguments for strong solutions of the 3D periodic Navier-Stokes equations, the authors show that if the pressure field P is assumed to be uniformly bounded for all t in L158+ in / ( in >0), then the Navier-Stokes equations are regular. The method of proof uses a so-called 'lattice theorem' which gives a set of differential inequalities for the quantities HN,m identical to //DNu//2m2m (m>or=1). As a parallel result, this thereom also gives Serrin's L3+ in regularity result for the velocity field.Keywords
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