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Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows. (English) Zbl 1091.35070
Summary: We consider the long time behavior of moments of solutions and of the solutions itself to dissipative quasi-geostrophic flow with subcritical powers. The flow under consideration is described by the nonlinear scalar equation \[ \frac{\partial\theta}{\partial t}+u\cdot\nabla \theta+\kappa(-\Delta)^\alpha\theta=f,\quad \theta|_{t=0}=\theta_0. \] Rates of decay are obtained for moments of the solutions, and lower bounds of decay rates of the solutions are established.

35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35B40 Asymptotic behavior of solutions to PDEs
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