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Pré-Publication, Document De Travail Année : 2022

Large, Global Solutions To The Three-Dimensional The Navier-Stokes Equations Without Vertical Viscosity

Résumé

The three-dimensional, homogeneous, incompressible Navier-Stokes equations are studied in the absence of viscosity in one direction. It is shown that there are arbitrarily large initial data generating a unique global solution, the main feature of which is that they are slowly varying in the direction where viscosity is missing. The difficulty arises from the complete absence of a regularising effect in this direction. The special structure of the nonlinear term, joint with the divergence-free condition on the velocity field, is crucial in obtaining the result.
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hal-03585502 , version 1 (23-02-2022)

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Isabelle Gallagher, Alexandre Yotopoulos. Large, Global Solutions To The Three-Dimensional The Navier-Stokes Equations Without Vertical Viscosity. 2022. ⟨hal-03585502⟩
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