论文标题
在傅立叶 - 纹期和负期的调制空间中的非线性schrodinger方程的标准通货膨胀
Norm inflation for nonlinear Schrodinger equations in Fourier-Lebesgue and modulation spaces of negative regularity
论文作者
论文摘要
我们考虑傅立叶 - lebesgue中的非线性schr {Ö} dinger方程，调制空间涉及负期。方程式在整个空间上构成，并涉及平稳的功率非线性。我们证明了两种类型的规范通货膨胀结果。我们首先建立低于预期关键规律的规范通货膨胀结果。然后，我们证明在不太一般的假设下，无限规律性丧失的规范通货膨胀。为此，我们在一般的抽象功能设置中重塑了非线性schr {Ö} dinger方程的多相弱非线性几何光学的理论。
We consider nonlinear Schr{ö}dinger equations in Fourier-Lebesgue and modulation spaces involving negative regularity. The equations are posed on the whole space, and involve a smooth power nonlinearity. We prove two types of norm inflation results. We first establish norm inflation results below the expected critical regularities. We then prove norm inflation with infinite loss of regularity under less general assumptions. To do so, we recast the theory of multiphase weakly nonlinear geometric optics for nonlinear Schr{ö}dinger equations in a general abstract functional setting.
