Journal of Mathematical Fluid Mechanics

, Volume 2, Issue 1, pp 16-98

First online:

On the Strong Solvability of the Navier—Stokes Equations

  • H. AmannAffiliated withInstitut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract.

In this paper we study the strong solvability of the Navier—Stokes equations for rough initial data. We prove that there exists essentially only one maximal strong solution and that various concepts of generalized solutions coincide. We also apply our results to Leray—Hopf weak solutions to get improvements over some known uniqueness and smoothness theorems. We deal with rather general domains including, in particular, those having compact boundaries.

Keywords. Weak, very weak, and strong solutions; existence and uniqueness theorems with rough initial data.