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Local in time regularity properties of the Navier-Stokes equations. (English) Zbl 1175.35100

For a weak solution \(u\) of the Navier-Stokes equations in a smooth domain of \({\mathbb R}^3\) in a time interval \([0,T)\) for \(0<T\leq \infty\), with initial value \(u_0\), the authors use new assumptions, beyond classical Serrin’s additional conditions, on \(u_0\) in order to prove various local and global regularity properties of \(u\).

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35B65 Smoothness and regularity of solutions to PDEs
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