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Zbl 0970.35105
Beirão da Veiga, Hugo
A sufficient condition on the pressure for the regularity of weak solutions to the Navier-Stokes equations.
(English)
[J] J. Math. Fluid Mech. 2, No.2, 99-106 (2000). ISSN 1422-6928; ISSN 1422-6952/e

For non-stationary incompressible Navier-Stokes equations in $\Omega\subset\bbfR^n$ with pressure $p$ and velocity $n$, the author shows that if ${p\over 1+|v|}\in L^r(0, T;L^q(\Omega))$ with ${2\over r}+{n\over q}= 1$, $q\in (n,+\infty)$, which is in formal agreement with the Poisson equation relating pressure and velocity, then $v\in C(0,T; H_\alpha(\Omega))$ and $|v|^{\alpha/2}\in L^2(0, T;H^1_0(\Omega))$.
[Oleg Titow (Berlin)]
MSC 2000:
*35Q30 Stokes and Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: sufficient condition on pressure; regularity of weak solutions; non-stationary incompressible Navier-Stokes equations; Poisson equation

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