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On the regularity of the pressure of weak solutions of Navier-Stokes equations. (English) Zbl 0574.35070
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 L. Caffarelli, R. Kohn and L.Nirenberg [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)] for the whole space.

MSC:
35Q30 Navier-Stokes equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35D05 Existence of generalized solutions of PDE (MSC2000)
76D05 Navier-Stokes equations for incompressible viscous fluids
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