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Zbl 0574.35070
Sohr, Hermann; von Wahl, Wolf
On the regularity of the pressure of weak solutions of Navier-Stokes equations. (English)
[J] Arch. Math. 46, 428-439 (1986). ISSN 0003-889X; ISSN 1420-8938/e

The aim of this paper is to prove the regularity property $p\in L\sp{5/3}$ 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 $\vert x\vert$ in an exterior domain. This result has been proved by {\it L. Caffarelli}, {\it R. Kohn} and {\it L.Nirenberg} [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)] for the whole space.

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
35D10 Regularity of generalized solutions of PDE
35D05 Existence of generalized solutions of PDE
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: regularity; pressure of weak solutions; Navier-Stokes equations; linearized equation; existence; weak solution

Citations: Zbl 0509.35067

Cited in: Zbl 1188.35129 Zbl 0958.35102

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