Marko Iosifovich Vishik

Trajectory Attractors for Dissipative 2D Euler and Navier-Stokes Equations

AbstractA trajectory attractor

Trajectory attractor for a system of two reaction-diffusion equations with diffusion coefficient δ(t) → 0+ as t → + ∞

\mathfrak{A}

Averaging of trajectory attractors of evolution equations with rapidly oscillating terms

is constructed for the 2D Euler system containing an additional dissipation term −ru, r > 0, with periodic boundary conditions. The corresponding dissipative 2D Navier-Stokes system with the same term −ru and with viscosity v > 0 also has a trajectory attractor,

Колмогоровская

\mathfrak{A}_\nu

-энтропия аттракторов систем реакции-диффузии@@@Kolmogorov

. Such systems model large-scale geophysical processes in atmosphere and ocean (see [1]). We prove that