, Volume 11, Issue 2, pp 355-398

Weak Solutions and Attractors for Three-Dimensional Navier–Stokes Equations with Nonregular Force

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Abstract

A three-dimensional Navier–Stokes equation is considered. The forcing term is the derivative of a continuous function; the case of white noise is also considered. The aim is to prove the existence of weak solutions and to construct an attractor for the corresponding shift dynamical system in path space, following an idea of Sell.