Holder regularity in time of solutions to the generalized surface quasi-geostrophic equation

In this paper, we are concerned with the Holder regularity in time of both solutions and their energy for the generalized surface quasi-geostrophic equation with the velocity v given by v = R perpendicular to Lambda gamma-1 theta. In the first part, it is shown that the regularity in time of solutions theta is Ct alpha for 0 < alpha < 1 with 0 < gamma < 1 and C alpha/gamma t for gamma - 1 < alpha < 1 with 1 < gamma < 2, as long as theta belongs to L infinity tCx alpha.In the second part, we address the Holder regularity in time of their energy and establish the corresponding criteria for the temperature in Onsager-subcritical spaces.(c) 2022 Elsevier Ltd. All rights reserved.