Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation

Abstract EN

We study the behavior at infinity in time of any global solution θ∈C(R+,Ḣ2-2α(R2)) of the surface quasigeostrophic equation with subcritical exponent 2/3≤α≤1.

We prove that limt→∞∥θ(t)∥Ḣ2-2α=0.

Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that if θ∈C(R+,Ḣ2-2α(R2)) is a global solution, then limt→∞∥θ(t)∥H2-2α=0.