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Article Dans Une Revue Journal of Fourier Analysis and Applications Année : 2020

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

Résumé

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.
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Dates et versions

hal-02560258 , version 1 (01-05-2020)
hal-02560258 , version 2 (05-09-2020)

Identifiants

Citer

Divyang G. Bhimani, Rémi Carles. Norm inflation for nonlinear Schrodinger equations in Fourier-Lebesgue and modulation spaces of negative regularity. Journal of Fourier Analysis and Applications, 2020, 26 (6), pp.n° 78. ⟨10.1007/s00041-020-09788-w⟩. ⟨hal-02560258v2⟩
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