Archive for Rational Mechanics and Analysis

, Volume 163, Issue 1, pp 65-86

First online:

Navier-Stokes Equations with Lower Bounds on the Pressure

  • G. SereginAffiliated withSteklov Institute of Mathematics at St.Petersburg¶St.Peterburg, Russia
  • , V. ŠverákAffiliated withSchool of Mathematics, University of Minnesota¶Minneapolis, USA

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We prove that weak solutions of the three-dimensional incompressible Navier-Stokes equations are smooth if the negative part of the pressure is controlled, or if the positive part of the quantity |v|2+ 2p is controlled.