Concerning the regularity of the solutions to the Navier-Stokes equations via the truncation method; Part I (Q1979026)

A new class of uniqueness for weak solutions of incompressible Navier-Stokes equations is discovered. Namely, if \(v\) and \(p\) denote velocity and pressure, respectively, then it is the set of all couples \((v,p)\) such that there exists \(k\in [0,\infty)\) for which \(|p|(1+|v|)^{-1}\in L^r(0,T;L^q(\{ x: |v(x,t)|>k\}))\). Here \(2r^{-1}+nq^{-1}=1\) with \(q\in (n,\infty ], n\) being the number of space variables, and \(T>0\) is any time of existence for the weak solution (which is known to exist globally).