Norm Inflation for Nonlinear Schrödinger Equations in Fourier–Lebesgue and Modulation Spaces of Negative Regularity - Bhimani, Divyang G.; Carles, Rémi (The Journal of fourier analysis and applications, 2020)
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.