Weighted energy inequalities for the navier-stokes equations in exterior domains

Abstract

Consider the nonstationary Navier-Stokes equations on an exterior domain in IR3. Under suitable assumptions on the initial value and the external force we prove the existence of a global, suitable weak solution satisfying a weighted energy inequality with weight functions |x|^α,0≤α≤1. This weak solution is constructed using the Yosida approximation procedure, Lg-theory and localized energy inequalities as int,roduced by Caffarelli, Kohn and Nirenberg [3].

Keywords:

• exterior domain
• generalized energy inequality
• instationary Navier-Stokes equations
• radially weighted norms
• suitable weak solutions
• weoghted energy inequality

Additional information

Notes on contributors

Reinhard Farwig