Abstract: | In the exterior domain Ω⊂ℝ2 we consider the two-dimensional Navier-stokes system Δu-▽p=(u,▽)u, div u=0 whose solution possesses a finite Dirichlet integral
and satisfies the condition lim|x|→∞
u(x)=(1, 0). For this solution, we establish the estimate |u(x)−(1, 0)|≤c|x|
−α, where α>1/4. This estimate implies an asymptotic expression for the solution indicating the presence of a track behind the
body.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 246–253, February, 1999. |