On Liouville type theorems for the steady Navier–Stokes equations in R3R3

In this paper we prove three different Liouville type theorems for the steady Navier–Stokes equations in R3R3. In the first theorem we improve logarithmically the well-known L92(R3) result. In the second theorem we present a sufficient condition for the trivially of the solution (v=0v=0) in terms of the head pressure, Q=12|v|2+p. The imposed integrability condition here has the same scaling property as the Dirichlet integral. In the last theorem we present Fubini type condition, which guarantee v=0v=0.