Decay of the 3D Lüst model

Abstract

AbstractIn 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 $\dot{H}^{-s}$ H ˙ − s ($0\leq s<\frac{3}{2}$ 0 ≤ s < 3 2 ) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.