二维色散Quasi-Geostrophic方程组的整体适定性

Global Well-Posedness of Two-Dimensional Dispersive Quasi-Geostrophic Equations

本文研究一类二维色散 quasi-geostrophic 方程组初值问题的整体适定性。 通过引进一类高低频具有不同正则性指标的混合型 Besov 空间,并通过建立相应的色散半群在其上的一致有界性估计,证明了该二维色散 quasi-geostrophic 方程组关于混合型临界 Besov 空间中一致小初值的整体适定性。

This paper is devoted to studying the global well-posedness of Cauchy problem for the two-dimensional dispersive quasi-geostrophic equations. By introducing a kind of Hybrid-Besov spaces with different regularity indices at high frequency and low frequency, and by establishing the uniformly bounded estimations of the corresponding dispersive operator semigroup on these new function spaces, the global well-posedness of the 2D dispersive quasi-geostrophic equations is obtained for uniformly small initial values in the critical functional framework.