Journal of the
Korean Mathematical Society JKMS

Consider a weak solution $u$ of the Navier-Stokes equations in the class $% L^{2}\left( \left( 0,T\right) ;\overset{.}{X}_{1}(\mathbb{R}^{d})^{d}\right) $. We establish a new approach to treat the regularity problem for the Navier-Stokes equation in term of the multiplier space $\overset{.}{X}_{1}(\mathbb{R}^{d})$.

Keywords: Navier-Stokes equations, weak solution, regularity, multiplier spaces

MSC numbers: 35B45, 35B65, 76D05