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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.

MSC:
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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