Resumo: The 2D Quasi-geostrophic equation attracts attention of mathematicians through recent years. While the sub-critical problems are rather standard (but not classical), the critical equation contains nonlinearity of the same order as the main dissipative half negative Laplace operator. Therefore we face a balance of the two terms in that case, which makes the problem interesting. We discuss existence of a weak solution of the critical problem, and associate it with a multivalued semiflow. A compact global attractor is shown to exist for that multivalued semiflow.
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