J$_{5}$ = s ∫ Ω | z | $^{2}$Δ$_{x}$ (Δ$_{y}$ ϕ − Δ$_{x}$ ϕ ) dxdydt, J$_{6}$ = 2 s 3 ∫ Ω | z | 2 ∇ $_{y}$ϕ · ∇ y ( |∇ $_{y}$ϕ | 2 − |∇ $_{x}$ϕ | 2 ) dxdydt − 2 s 3 ∫ Ω | z | 2 ∇ $_{x}$ϕ · ∇ x ( |∇ $_{y}$ϕ | 2 − |∇ $_{x}$ϕ | 2 ) dxdydt and B$_{0}$ = − 2 s Im ∫ Γ$_{y}$ z∂$_{t}$z ( ∇ $_{y}$ϕ · ν ) dS$_{y}$dxdt +4 s Re Γ$_{y}$ ( ∂$_{ν}$z ) ( ∇ $_{x}$ϕ · ∇ $_{x}$z − ∇ $_{y}$ϕ · ∇ $_{y}$z ) dS$_{y}$dxdt +2 s ∫ Γ$_{y}$ ( ∂$_{ν}$ϕ ) ( |∇ $_{y}$z | 2 − |∇ $_{x}$z | 2 ) dS$_{y}$dxdt − 2 s 3 Γ$_{y}$ ( ∂$_{ν}$ϕ ) | z | 2 ( |∇ $_{y}$ϕ | 2 − |∇ $_{x}$ϕ | 2 ) dS$_{y}$dxdt − 2 s ∫ Γ$_{y}$ ( ∂$_{ν}$z ) (Δ$_{y}$ ϕ − Δ$_{x}$ ϕ ) zdS$_{y}$dxdt + s ∫ Γ$_{y}$ ∂$_{ν}$ (Δ$_{y}$ ϕ − Δ$_{x}$ ϕ ) | z | 2 dS$_{y}$dxdt +2 s Im ∫ Γ$_{x}$ z∂$_{t}$z ( ∇ $_{x}$ϕ · ν ) dS$_{x}$dydt +4 s Re Γ$_{x}$ ( ∂$_{ν}$z ) ( ∇ $_{y}$ϕ · ∇ $_{y}$z − ∇ $_{x}$ϕ · ∇ $_{x}$z ) dS$_{x}$dydt − 2 s ∫ Γ$_{x}$ ( ∂$_{ν}$ϕ ) ( |∇ $_{y}$z | 2 − |∇ $_{x}$z | 2 ) dS$_{x}$dydt +2 s 3 Γ$_{x}$ ( ∂$_{ν}$ϕ ) | z | 2 ( |∇ $_{y}$ϕ | 2 − |∇ $_{x}$ϕ | 2 ) dS$_{x}$dydt +2 s ∫ Γ$_{x}$ ( ∂$_{ν}$z ) (Δ$_{y}$ ϕ − Δ$_{x}$ ϕ ) zdS$_{x}$dydt − s ∫ Γ$_{x}$ ∂$_{ν}$ (Δ$_{y}$ ϕ − Δ$_{x}$ ϕ ) | z | 2 dS$_{x}$dydt. Next, we shall estimate J$_{k}$, 1 ≤ k ≤ 6 and B$_{0}$ using the following elemantary properties of the weight function: 12 ∂$_{t}$ϕ = ( − 2 γβt ) ϕ, ϕ$_{x}$$_{i}$$_{y}$$_{j}$ = γ $^{2}$ϕψ$_{x}$$_{i}$ ψ$_{y}$$_{j}$ , ϕ$_{y}$$_{i}$$_{y}$$_{j}$ = γϕ ( ψ$_{y}$$_{i}$$_{y}$$_{j}$ + γψ$_{y}$$_{i}$ψ$_{y}$$_{j}$ ) , ∇ $_{y}$ϕ = γϕ ∇ $_{y}$ψ, ∂$_{t}$ ( ∇ $_{y}$ϕ ) = ( − 2 γ $^{2}$βt ) ϕ ∇ $_{y}$ψ, Δ$_{y}$ ϕ = γϕ ( Δ$_{y}$ ψ + γ |∇ $_{y}$ψ | 2 ) , ϕ$_{x}$$_{i}$$_{x}$$_{i}$ = γϕ ( 2 + γψ 2 x$_{i}$ ) , ϕ$_{x}$$_{i}$$_{x}$$_{j}$ = γϕ ( ψ$_{x}$$_{i}$$_{x}$$_{j}$ + γψ$_{x}$$_{i}$ψ$_{x}$$_{j}$ ) , ∇ $_{x}$ϕ = γϕ ∇ $_{x}$ψ, ∂$_{t}$ ( ∇ $_{x}$ϕ ) = ( − 2 γ $^{2}$βt ) ϕ ∇ $_{x}$ψ, Δ$_{x}$ ϕ = γϕ ( Δ$_{x}$ ψ + γ |∇ $_{x}$ψ | 2 ) , Δ$_{y}$ ϕ − Δ$_{x}$ ϕ = γϕd$_{1}$ ( ψ ) + γ $^{2}$ϕd$_{2}$ ( ψ ) ,