导数非线性Schrödinger方程的先验估计

Pub Date : 2020-07-26 DOI:10.1619/fesi.65.329

Friedrich Klaus, R. Schippa

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引用次数: 10

摘要

我们证明了Besov空间中导数非线性薛定谔方程的低正则性先验估计，该方程的正正则性指数以小$L^2$-范数为条件。这涵盖了整个亚临界范围。对于完全可积PDE，我们使用Killip–Visan–Zhang引入的扰动行列式的幂级数展开。这使得从扰动行列式中导出低正则守恒定律成为可能。

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A Priori Estimates for the Derivative Nonlinear Schrödinger Equation

We prove low regularity a priori estimates for the derivative nonlinear Schrodinger equation in Besov spaces with positive regularity index conditional upon small $L^2$ -norm. This covers the full subcritical range. We use the power series expansion of the perturbation determinant introduced by Killip–Visan–Zhang for completely integrable PDE. This makes it possible to derive low regularity conservation laws from the perturbation determinant.

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