Abstract
In this paper, we establish the local well-posedness for the quasi-geostrophic equations and obtain a blow-up criterion of smooth solutions in the framework of Triebel-Lizorkin-Lorentz spaces by adapting a method in Chen-Miao-Zhang (Arch. Rational Mech. Anal. 195: 2010, 561–578). Our new function spaces contain the classical Triebel-Lizorkin spaces and Sobolev spaces, and thus the corresponding results generalize several known ones, for instance, Chae (Nonlinearity 16: 2003, 479–495) and Castro et al. (Nonlinearity 22: 2009, 1791–1815). The main ingredients of our proofs are Littlewood–Paley decomposition and the paradifferential calculus.
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Xiang, Z., Yan, W. On the well-posedness of the quasi-geostrophic equation in the Triebel-Lizorkin-Lorentz spaces. J. Evol. Equ. 11, 241–263 (2011). https://doi.org/10.1007/s00028-010-0090-y
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DOI: https://doi.org/10.1007/s00028-010-0090-y