1. College of Science, National University of Defense Technology, Changsha, 410073, PR China;2. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, PR China
Abstract:
The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than as time t goes to infinity. This improves the works of Selberg and da Silva (2017) 30] and Tesfahun (2017) 34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.