We consider nonlinear Schrödinger 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 Schrödinger equations in a general abstract functional setting.

中文翻译：

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负规则性的Fourier-Lebesgue和调制空间中非线性Schrödinger方程的范数膨胀

我们考虑傅立叶-莱贝格和涉及负正则性的调制空间中的非线性薛定ding方程。这些方程式构成了整个空间，并涉及平滑的功率非线性。我们证明两种类型的标准通货膨胀结果。我们首先建立低于预期关键规律的正常通胀结果。然后，我们在不太笼统的假设下证明了规则膨胀，同时又失去了规律性。为此，我们在一般的抽象函数环境中重塑了非线性Schrödinger方程的多相弱非线性几何光学理论。