Publications (2)0.73 Total impact
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ABSTRACT: The regularity of solutions to a large class of analytic nonlinear parabolic equations on the two-dimensional sphere is considered. In particular, it is shown that these solutions belong to a certain Gevrey class of functions, which is a subset of the set of real analytic functions. As a consequence it can be shown that the Galerkin schemes, based on the spherical harmonics, converge exponentially fast to the exact solutions, as the number of modes involved in the approximation tends to infinity. Furthermore, in the case that the underlying evolution equation has a global attractor, then this global attractor is contained in the space of spatially real analytic functions whose radii of analyticity are bounded uniformly from below.Journal of Dynamics and Differential Equations 01/2000; 12(2):411-433. · 0.73 Impact Factor
Article: The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom[show abstract] [hide abstract]
ABSTRACT: In this article we prove a Gevrey class global regularity to the Navier-Stokes equations on the rotating two dimensional sphere, S 2 -a fundamental model that arises naturally in large scale atmospheric dynamics. As a result one concludes the exponential convergence of the spectral Galerkin numerical method, based on spherical harmonic functions. Moreover, we provide an upper bound for the number of asymptotic degrees of freedom for this system. Mathematics Subject Classification (1991). 35Q30, 76D05, 76U05, 58G11, 86Axx. Keywords. Gevrey regularity, Navier−Stokes equations on the sphere, geophysical flows, de-termining degrees of freedom.Math. Phys. 01/1999; 50:341-360.