Global well-posedness for the critical dissipative quasi-geostrophic equations in L∞

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Abstract

In this paper, we study the critical dissipative quasi-geostrophic equations in scaling invariant spaces. We prove that there exists a global-in-time small solution for small initial data θ0∈L∞∩ H1 such that (θ0)∈L∞, where is the Riesz transform. As a corollary, we prove that if in addition, θ0∈B∞,q0, 1≤q<2, is small enough, then θ∈Lt∞B∞,q0∩Lt1B∞,q1. © 2010 Elsevier Ltd. All rights reserved.

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Bae, H. (2011). Global well-posedness for the critical dissipative quasi-geostrophic equations in L∞. Nonlinear Analysis, Theory, Methods and Applications, 74(5), 1995–2002. https://doi.org/10.1016/j.na.2010.11.006

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