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On strong solutions of Navier-Stokes equations with two velocity components
AIMS Mathematics 2026, 11(4): 9334-9346
Published: 07 April 2026
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In this paper, we established a continuation criterion for local strong solutions to the three-dimensional incompressible Navier-Stokes equations based on partial velocity components. More precisely, we showed that a unique local strong solution u does not blow up at time T provided that the two horizontal velocity components u h belong to the Banach spaces V ˙ p , q , θ s and U ˙ p , β , σ s . These functional spaces strictly contained the homogeneous Besov space B ˙ p , q s , and thus allowed a wider admissible class than those considered in earlier works. Our results can therefore be viewed as an extension and refinement of previously known criteria.

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