Journal of Mathematical Fluid Mechanics

, Volume 9, Issue 4, pp 533–542 | Cite as

A Remark on L Solutions to the 2-D Navier–Stokes Equations

  • Okihiro SawadaEmail author
  • Yasushi Taniuchi


A single-exponential growth estimate of the solutions to the 2-dimensional Navier–Stokes equations in the whole space for nondecaying initial velocity is established. The crucial idea is to decompose velocity into high and low frequency parts. Moreover, if the linear term and the vorticity decay exponentially, the velocity is bounded uniformly in time.

Mathematics Subject Classification (2000).

35Q30 35Q35 


2-dimensional Navier–Stokes nondecaying initial velocity vanishing viscosity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhaueser 2006

Authors and Affiliations

  1. 1.Department of Mathematical ScienceWaseda UniversityShinjukuJapan
  2. 2.Department of Mathematical SciencesShinshu UniversityMatsumotoJapan

Personalised recommendations