A sufficient condition on the pressure for the regularity of weak solutions to the Navier-Stokes equations. (English) Zbl 0970.35105

Beirão da Veiga, Hugo

J. Math. Fluid Mech. 2, No. 2, 99-106 (2000).

For non-stationary incompressible Navier-Stokes equations in \(\Omega\subset\mathbb{R}^n\) 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 \(|v|^{\alpha/2}\in L^2(0, T;H^1_0(\Omega))\).

Reviewer: Oleg Titow (Berlin)

MSC:

35Q30	Navier-Stokes equations
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

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