The sharp Strichartz and Sobolev-Strichartz inequalities for the fourth-order Schrödinger equation

In this paper, we will obtain that there exists a maximizer for the non-endpoint Strichartz inequalities for the fourth-order Schrodinger equation with initial data in the L2(Rd) space in all dimensions, and then we obtain a maximizer also for the non-endpoint Sobolev–Strichartz inequality for the fourth-order Schrodinger equation with initial data in the homogeneous Sobolev space. Our analysis derived from the linear profile decomposition. Copyright © 2014 John Wiley & Sons, Ltd.