On the other hand, since and we have We see that there exists a constant γ$_{1}$ such that for arbitrary γ > γ$_{1}$, the terms of X$_{1}$ and X$_{5}$ can be absorbed by 64 δ 2 $_{0}$s$^{3}$γ 4 ∫ Ω ϕ 3 | z | $^{2}$dxdydt , and we have Since ϕ > 0 on ¯ Ω for γ > γ$_{1}$, there exist constants C$_{5}$ = C$_{5}$ ( γ ) and s$_{1}$ = s$_{1}$ ( γ ) such that for all s > s$_{1}$, 21 − 2 Re ∫ Ω (4 α + µ ) sγ ( P$_{s}$z + is∂$_{t}$ϕz ) ϕzdxdydt ≤ (4 α + µ ) ∫ Ω | P$_{s}$z + is∂$_{t}$ϕz | $^{2}$dxdydt + C$_{1}$s 2 ∫ Ω | z | $^{2}$dxdydt ‖ P$_{s}$z + is∂$_{t}$ϕz ‖ 2 L $^{2}$(Ω) = ∥ P + s z ∥ 2 L $^{2}$(Ω) + ∥ P − s z ∥ 2 L $^{2}$(Ω) + 2 Re ( P + s z, P − s z ) L $^{2}$(Ω) , C$_{2}$ ∫ Ω | P$_{s}$z + is∂$_{t}$ϕz | $^{2}$dxdydt ≥ ∫ Ω ∣ P + s z ∣ $^{2}$dxdydt + ∫ Ω ∣ P − s z ∣ $^{2}$dxdydt +2 sγC$_{3}$ ∫ Ω ϕ |∇ $_{x}$z | $^{2}$dxdydt + 2 sγC$_{4}$ ∫ Ω ϕ |∇ $_{y}$z | 2 dxdydt +64 δ 2 $_{0}$s$^{3}$γ 4 ∫ Ω ϕ 3 | z | $^{2}$dxdydt + B$_{0}$ + X$_{1}$ + X$_{2}$ + X$_{5}$ + X$_{6}$. C$_{2}$ ∫ Ω | P$_{s}$z + is∂$_{t}$ϕz | $^{2}$dxdydt ≥ ∫ Ω ∣ P + s z ∣ $^{2}$dxdydt + ∫ Ω ∣ P − s z ∣ $^{2}$dxdydt +2 sγC$_{3}$ ∫ Ω ϕ |∇ $_{x}$z | $^{2}$dxdydt + 2 sγC$_{4}$ ∫ Ω ϕ |∇ $_{y}$z | 2 dxdydt +64 δ 2 $_{0}$s$^{3}$γ 4 ∫ Ω ϕ 3 | z | $^{2}$dxdydt + B$_{0}$ + X$_{2}$ + X$_{6}$. C$_{2}$ ∫ Ω | P$_{s}$z + is∂$_{t}$ϕz | $^{2}$dxdydt ≥ ∫ Ω ∣ P + s z ∣ $^{2}$dxdydt + ∫ Ω ∣ P − s z ∣ $^{2}$dxdydt + C$_{5}$ ( γ ) s ∫ Ω |∇ $_{x}$z | $^{2}$dxdydt + C$_{5}$ ( γ ) s ∫ Ω |∇ $_{y}$z | $^{2}$dxdydt + C$_{5}$ ( γ ) s 3 Ω | z | 2 dxdydt + B$_{0}$ + X$_{2}$ + X$_{6}$.