Decay estimates and limit behaviour of fractional fourth Schr\"odinger Equation

Abstract

In this paper, we study the linear version  for the one-dimensional fourth order Schrödinger equation with the term $i^\al$. The first contribution is of considering the decay properties of the mild solution. Some other contributions is of study the convergence rate of the solution when the parameters tends to zero or $1^-$. This current paper is motivated by the interesting paper [The linear profile decomposition for the fourth order Schrödinger equation. J. Differential Equations 249 (2010), no. 10, 2521--2547].