Abstract
We consider three-dimensional incompressible Navier-Stokes equations (NS) with different viscous coefficients in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared with the initial data, we prove the global well-posedness of this system. In fact, we obtain the existence of a global strong solution to (NS) when the initial data verifies an anisotropic smallness condition which takes into account the different roles of the horizontal and vertical viscosity.
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Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday
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Paicu, M., Zhang, P. Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction. Sci. China Math. 62, 1175–1204 (2019). https://doi.org/10.1007/s11425-018-9504-1
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DOI: https://doi.org/10.1007/s11425-018-9504-1