Global well-posedness to the two-dimensional incompressible vorticity equation in the half plane

This paper is concerned with the global well-posedness of two-dimensional incompressible vorticity equation in half plane. Under assumption that initial ω0∈Wk,p(R+2) k≥3 an integer and 10. An elementary self-contained proof presented delicate estimates velocity its derivatives are obtained this paper. It should be emphasized uniform estimate on ∫0t‖∇u(τ)‖L∞(R+2)dτ required to complete regularity solution. To do that, double exponential growth time gradient plane established applied. different from Euler equations Sobolev spaces, which Kato-type or logarithmic-type enough close energy estimates.