Regularity criterion on weak solutions to the Navier-Stokes equations. (English) Zbl 1221.35277

Gala, Sadek

J. Korean Math. Soc. 45, No. 2, 537-558 (2008).

Consider a weak solution \(u\) of the Navier-Stokes equations in the class \(L^2((0,T);\dot X_1(\mathbb{R}^d)^d)\). We establish a new approach to treat the regularity problem for the Navier-Stokes equation in terms of the multiplier space \(\dot X_n(\mathbb{R}^d)\).

Reviewer: Pavel Burda (Praha)

MSC:

35Q30	Navier-Stokes equations
35B45	A priori estimates in context of PDEs
35B65	Smoothness and regularity of solutions to PDEs
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

weak solution; Navier-Stokes equations; regularity; multiplier space