Extremizers for the Strichartz Inequality for a Fourth-Order Schrödinger Equation

In this paper, we consider the Strichartz inequality for a fourth-order Schrödinger equation on ${\mathbb{R}}^{2+1}$. We show that extremizers exist using a linear profile decomposition which follows from the endpoint version decomposition and the stationary phase method. Based on the existence of extremizers, we investigate the associated Euler-Lagrange equation to show that the extremizers have exponential decay and consequently must be analytic.