Long-time decay to the global solution of the 2D dissipative quasigeostrophic equation (Q437593)

Summary: The authors study the behavior at infinity in time of any global solution \(\theta \in \mathcal C(\mathbb R^+, H^{2-2\alpha}(\mathbb R^2))\) of the surface quasigeostrophic equation with subcritical exponent \(2/3 \leq \alpha \leq 1\). They prove that \(\lim_{t \rightarrow \infty} ||\theta(t)||_{H^{2-2\alpha}} = 0\). Moreover, they prove the nonhomogeneous version of the previous result, and that if \(\theta \in \mathcal C(\mathbb R^+, H^{2-2\alpha}(\mathbb R^2))\) is a global solution, then \(\lim_{t \rightarrow \infty} ||\theta(t)||_{H^{2-2\alpha}} = 0\).