Relative Decay Conditions on Liouville Type Theorem for the Steady Navier-Stokes System

초록

In this paper we prove Liouville type theorem for the stationary Navier-Stokes equations in R-3 under the assumptions on the relative decays of velocity, pressure and the head pressure. More precisely, we show that any smooth solution (u, p) of the stationary Navier-Stokes equations satisfying u(x) -> 0 as vertical bar x vertical bar -> +infinity and the condition of finite Dirichlet integral integral(R3) vertical bar del u vertical bar(2)dx < +infinity is trivial, if either vertical bar u(x)vertical bar/vertical bar Q(x)vertical bar = O(1) or vertical bar p(x)vertical bar/vertical bar Q(x)vertical bar = O(1) as vertical bar x vertical bar -> infinity, where vertical bar Q vertical bar = 1/2 vertical bar u vertical bar 2 + p is the head pressure.

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