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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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