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We address the decay of the norm of weak solutions to the 2D dissipative quasi-geostrophic equation. When the initial data θ 0 is in L 2 only, we prove that the L 2 norm tends to zero but with no uniform rate, that is, there are solutions with arbitrarily slow decay. For θ 0 in L p ∩ L 2 , with 1 ≤ p < 2, we are able to obtain a uniform decay rate in L 2.(More)
For many classes of symplectic manifolds, the Hamiltonian flow of a function with sufficiently large variation must have a fast periodic orbit. This principle is the base of the notion of Hofer-Zehnder capacity and some other symplectic invariants and leads to numerous results concerning existence of periodic orbits of Hamiltonian flows. Along these lines,(More)
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