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arXiv · 2210.06695

Extremizers for the Strichartz Inequality for a Fourth-Order Schr\"odinger Equation

Boning Di·Ryan Frier
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Abstract

In this paper, we consider the Strichartz inequality for a fourth-order Schr\"odinger 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.

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Boning Di, Ryan Frier. 2022-10-13. Extremizers for the Strichartz Inequality for a Fourth-Order Schr\"odinger Equation. https://arxiv.org/abs/2210.06695

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