## The tridimensional Navier-Stokes equations with almost bidimensional data: Stability, uniqueness, and life span.(English)Zbl 0893.35098

One considers the 3D incompressible Navier-Stokes equations in the case when there are two different viscosities: horizontal and vertical viscosities. The main purpose is to study the behaviour of the solutions of these equations when the initial data converges to a two-dimensional field. One proves that, for suitable conditions, the “finite energy solution” of $$3D$$ Navier-Stokes equations approaches the solution of a particular $$2D$$ Navier-Stokes equation i.e. the velocity field has three components which depend of two spatial variables.
Reviewer: V.A.Sava (Iaşi)

### MSC:

 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 35D05 Existence of generalized solutions of PDE (MSC2000)
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