Biswas, Animikh2024-11-142024-11-142014-06-13Biswas, Animikh. “Gevrey Regularity for the Supercritical Quasi-Geostrophic Equation.” Journal of Differential Equations 257, no. 6 (September 15, 2014): 1753–72. https://doi.org/10.1016/j.jde.2014.05.013.https://doi.org/10.1016/j.jde.2014.05.013http://hdl.handle.net/11603/36884In this paper, following the techniques of Foias and Temam, we establish suitable Gevrey class regularity of solutions to the supercritical quasi-geostrophic equations in the whole space, with initial data in “critical” Sobolev spaces. Moreover, the Gevrey class that we obtain is “near optimal” and as a corollary, we obtain temporal decay rates of higher order Sobolev norms of the solutions. Unlike the Navier–Stokes or the subcritical quasi-geostrophic equations, the low dissipation poses a difficulty in establishing Gevrey regularity. A new commutator estimate in Gevrey classes, involving the dyadic Littlewood–Paley operators, is established that allow us to exploit the cancellation properties of the equation and circumvent this difficulty.19 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Gevrey regularityQuasigeostrophic equationsTime decayText