AN ANALYSIS OF THE PRESSURE TERM IN THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH BOUNDED INITIAL DATA

In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations in R-n, n >= 3, for nondecaying initial data. First, this paper provides an analysis of the nondecaying (BMO) pressure term in the incompressible Navier-Stokes equations that appears in the paper [11] by H. O. Kreiss and J. Lorenz. Next, this paper considers a smooth periodic initial data and formally derives a periodic pressure term to analyze a relationship between these two pressure terms in the Cauchy problems with two slightly different initial data. This overall phenomenon is interesting, since these two pressure terms are closely related to each other, despite their fundamentally different representations.