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

Gallagher, Isabelle

Int. Math. Res. Not. 1997, No. 18, 919-935 (1997).

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)

Keywords:

Navier-Stokes equations; finite entropy solution; horizontal and vertical viscosities