On the maximum modulus theorem for stokes functions

Abstract

The following pointwise maximum modulus theorem for the Stokes system in dimension 2 is proven. Suppose that v is a Stokes function in the unit disc with corresponding pressure p, i.e., D) with

, such that v is continuous on Then, for x ∊D,

This result is shown via a Stokes-Poisson integral formula using Parseval's identity for Fourier series. A consequence of this pointwise estimate is the global estimate (“maximum modulus theorem”)

Keywords:

• Stokes System
• Stokes-Poisson integral formula
• maximum modulus theorem