Norm inflation for nonlinear Schrodinger equations in Fourier-Lebesgue and modulation spaces of negative regularity

Abstract

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.

27 pages. Two references added, some typos fixed

References in corpus (10)

• Ill-posedness for nonlinear Schrodinger and wave equations
• Local well-posedness of nonlinear dispersive equations on modulation spaces
• Loss of regularity for supercritical nonlinear Schrodinger equations
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• Geometric optics and instability for NLS and Davey-Stewartson models
• On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p,q}(\mathbb{R})$
• Multiphase weakly nonlinear geometric optics for Schrodinger equations
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Cited by in corpus (4)

• On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data
• Global well-posedness and equicontinuity for mKdV in modulation spaces
• Sobolev norms of $L^2$-solutions to NLS
• Norm inflation for BBM equation in Fourier amalgam and Wiener amalgam spaces with negative regularity