Asymptotic behavior of the solution to the two-dimensional stationary problem of flow past a body far from it

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.