Decay of the 3D Lüst model

Abstract

In this paper, we consider the time-decay rate of the strong solution to the Cauchy problem for the three-dimensional Lüst model. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The dot{H}^{-s} (0leq s<frac{3}{2}) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.