Linear profile decompositions for a family of fourth order Schrödinger equations

Linear profile decompositions for a family of fourth order Schrödinger equations
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四阶薛定谔方程族的线性轮廓分解

DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Betsy Stovall
Betsy Stovall
中科院分区：
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文献类型：
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作者：
Jin;Shuanglin Shao;Betsy Stovall

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我们建立了四阶薛定谔方程和薛定谔方程的某些四阶扰动的线性轮廓分解，维度大于或等于二。我们应用这些结果来证明相关 Stein--Tomas/Strichartz 不等式的极端化存在的二分法结果；在此过程中，我们还获得了这些算子规范的下界。
We establish linear profile decompositions for the fourth order Schr"odinger equation and for certain fourth order perturbations of the Schr"odinger equation, in dimensions greater than or equal to two. We apply these results to prove dichotomy results on the existence of extremizers for the associated Stein--Tomas/Strichartz inequalities; along the way, we also obtain lower bounds for the norms of these operators.