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A regularity criterion for the Navier-Stokes equations in the multiplier spaces. (English) Zbl 1242.35188

Summary: We exhibit a regularity condition concerning the pressure gradient for the Navier-Stokes equations in a special class. It is shown that if the pressure gradient belongs to \(L^{2/(2-r)}((0, T); \mathcal M(\dot{H}^r(\mathbb R^3) \rightarrow \dot{H}^{-r}(\mathbb R^3)))\), where \(\mathcal M(\dot{H}^r(\mathbb R^3) \rightarrow \dot{H}^{-r}( \mathbb R^3))\) is the multipliers between Sobolev spaces whose definition is given later for \(0 < r < 1\), then the Leray-Hopf weak solution to the Navier-Stokes equations is actually regular.

MSC:

35Q30 Navier-Stokes equations
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