On the regularity of the pressure of weak solutions of Navier-Stokes equations
The aim of this paper is to prove the regularity property \(p\in L^{5/3}\) for the pressure of weak solutions of Navier-Stokes equations in a bounded or an exterior domain. This result was known only for the whole space. The method to prove this property uses a new potential theoretical estimate of the linearized equation with different integration exponents in space and time. Using this regularity property of the pressure, it is possible to prove the existence of a weak solution of Navier-Stokes equations which is smooth for large \(| x|\) in an exterior domain. This result has been proved by \textit{L. Caffarelli}, \textit{R. Kohn} and \textit{L.Nirenberg} [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)] for the whole space.
scientific article; zbMATH DE number 3916871