Controllability of systems of Stokes equations with one control force : existence of insensitizing controls

Sergio Guerrero

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Conditions of Prodi-Serrin's type for local regularity of suitable weak solutions to the Navier-Stokes equations

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In the context of suitable weak solutions to the Navier-Stokes equations we present local conditions of Prodi-Serrin’s type on velocity $𝐯$ and pressure $p$ under which $(𝐱_{0}, t_{0}) \in Ω \times (0, T)$ is a regular point of $𝐯$ . The conditions are imposed exclusively on the outside of a sufficiently narrow space-time paraboloid with the vertex $(𝐱_{0}, t_{0})$ and the axis parallel with the $t$ -axis.

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