ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: not given Soltanov, Kamal N., Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan On some modification of Navier–Stokes equations We consider the problem (see [1])

\frac{∂u_{k}}{∂t} − ∑_{i=1}^{n} D_{i} (|u_{k}|^{p_{i}−2}D_{i}u_{k}) + ∑_{i=1}^{n} u_{i}D_{i}u_{k} + D_{k}p = h_{k}(x) , k = \overline{1, n} (1)

div u = 0 , (x, t) ∈ Ω × (0, T) ,  (2)
u(x, 0) = 0 , u|_{Γ} = 0 , Γ = ∂Ω × (0, T) ,  (3)

here Ω ∈ R^{n}(n ≥ 1) is bounded domain with smooth boundary ∂Ω. We prove uniqueness and solvability theorems.

[1] J. -L. Lions, Quelque méthodes …, 1969, Paris.