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Regularity criterion on weak solutions to the Navier-Stokes equations. (English) Zbl 1221.35277
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 $$\dot X_n(\mathbb{R}^d)$$.

##### 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
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